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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.
836:
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. (
750:
911:"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. (Fig. 826.02A)
914:
His modular dissection of a space-filling tetrahedron or MITE (minimum tetrahedron) into 2 A and 1 B module serves 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 is reminiscent of
866:
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
835:
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
891:
For example, his sphere packing studies led him to generalize a formula for polyhedral numbers: 2 P F + 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
803:
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
188:
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
861:
Fuller's geometric explorations provide an experiential basis for designing and refining a philosophical language. His overarching concern is the co-occurring relationship between tensile and compressive tendencies within an eternally regenerative
Universe. "Universe" is a proper name he defines in
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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 ... Synergetics follows the cosmic logic of
903:
The
Jitterbug Transformation provides a unifying dynamic in this work, with much significance attached to the doubling and quadrupling of edges that occur, when a cuboctahedron is collapsed through icosahedral, octahedral and tetrahedral stages, then inside-outed and re-expanded in a complementary
830:
A third consequence of switching to tetrahedral mensuration is 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
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The IVM scaffolding or skeletal framework is 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
189:
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.'"
907:
He models 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
124:
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
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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 catalogues the central and surface angles of these
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Synergetics also distinguishes 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
132:
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
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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)
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Synergetics does not aim to replace or invalidate pre-existing geometry or mathematics, as evidenced by the opening dedication to H.S.M. Coxeter, whom Fuller considered the greatest geometer of his era. Fuller acknowledges his vocabulary is "remote" even while defending his word choices.
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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.
904:
fashion. The JT forms a bridge between 3,4-fold rotationally symmetric shapes, and the 5-fold family, such as a rhombic triacontahedron, which later he analyzes in terms of the T module, another tetrahedral wedge with the same volume as his A and B modules.
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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)
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defined by four closest-packed unit-radius spheres. This tetrahedron anchors a set of concentrically arranged polyhedra proportioned in a canonical manner and inter-connected by a twisting-contracting, inside-outing dynamic that Fuller named the
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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.
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U = MP describes 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)
125:
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
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minimal starting point for spatial cognition. His use of "4D" is in many passages close to synonymous with the ordinary meaning of "3D," with the dimensions of physicality (time, mass) considered additional dimensions.
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Tetrahedral mensuration also involves substituting what Fuller calls the "isotropic vector matrix" (IVM) for the standard XYZ coordinate system, as his principal conceptual backdrop for special case physicality:
783:) The relative size of a shape is 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." (
82:
His oeuvre inspired many developers to further pioneer offshoots from synergetics, especially geodesic dome and dwelling designs. Among Fuller's contemporaries were Joe Clinton (NASA), Don Richter (Temcor),
79:", synergetics remains an off-beat subject, ignored for decades by most traditional curricula and academic departments, a fact Fuller himself considered evidence of a dangerous level of overspecialization.
55:
Since systems are identifiable at every scale, synergetics is necessarily interdisciplinary, embracing a broad range of scientific and philosophical topics, especially in the area of geometry, wherein the
1154:
E.J. Applewhite. The Naming of Buckminsterfullerene. The Chemical Intelligencer, July, 1995 (Vol. 1, No. 3), edited by Istvan Hargittai (Institute of General and Analytical Chemistry, Budapest Technical
167:
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. (See Sec. 1043.00.)
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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.
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Prime means sizeless, timeless, subfrequency. Prime is prehierarchical. Prime is prefrequency. Prime is generalized, a metaphysical conceptualization experience, not a special case.... (
283:
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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.
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in order to suggest where his A & B modules (depicted above), and by extension, many of his other concepts, might enter the mathematical literature (see Fig. 950.12).
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Generalized principles (scientific laws), although communicated energetically, do not inhere in the "special case" episodes, are considered "metaphysical" in that sense.
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The integration of geometry and philosophy in a single conceptual system providing a common language and accounting for both the physical and metaphysical.
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terms of "partially overlapping scenarios" while avoiding any static picture or model of same. His Universe is "non-simultaneously conceptual":
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extended synergetics to applications in social dynamics, and J.F. Nystrom proposed a theory of computational cosmography. Research continues.
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study of systems in transformation, with an emphasis on whole system behaviors unpredicted by the behavior of any components in isolation.
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to think of a unit shape "outside of which there must be something," or "within which, at center, there must be a smaller something." (
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Corresponding to Fuller's use of a regular tetrahedron as his unit of volume is his replacing the cube as his model of 3rd powering.(
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787:) Shapes not having any size, because purely conceptual in the Platonic sense, are "prefrequency" or "subfrequency" in contrast.
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nuanced term in the synergetics vocabulary, relating to the behavior of gyroscopes, but also to side-effects. (326.13, 1009.92)
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Fuller originally achieved more acceptance in the humanities as a poet-philosopher and architect. For example, he features in
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later cellular automaton studies in that tessellating modules would affect their neighbors over successive time intervals.
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Adam Rome. Spaceship Earth: Five Books that Pinpointed Our Planetary Limits. Nature Magazine. November 26, 2015. pg. 443.
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2" in this formula to the convex versus concave aspects of shapes, and to their polar spinnability respectively.
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Omnirationality: the identification of triangling and tetrahedroning with second- and third-powering factors.
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E.J. Applewhite, Cosmic Fishing: An Account of Writing Synergetics With Buckminster Fuller. Macmillan, 1977.
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behaviors not predicted by the behaviors of its parts, or as another term for negative entropy —
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A major error, caught by Fuller himself, involved a misapplication of his Synergetics Constant in
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52:, in collaboration with E. J. Applewhite, distills a lifetime of research into book form.
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by Hugh Kenner published in 1971, prior to the publication of Synergetics. The journal
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Presentation to the American Mathematical Society (AMS) 2008 Spring Eastern Meeting
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the definition of physical. Metaphysical is always generalized principle.(
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1169:. Department of Electrical and Computer Engineering, University of Idaho.
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Fuller hoped to gain traction for his nomenclature in part by dedicating
1167:"Tensional computation: Further musings on the computational cosmograph"
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this matrix have prefrequency volumes 1 and 4 respectively (see above).
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A chief hallmark of this system of mensuration is its unit of volume: a
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A Fuller Explanation: The Synergetic Geometry of R. Buckminster Fuller
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The rational volumetric quantation or constant proportionality of the
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and Ed Popko have published primers that help popularize synergetics,
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1361:, Vol. 1 in 1975 (with a preface and contribution by Arthur L. Loeb;
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discussing its overlap with crystallography, chemistry and virology.
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Here's an abridged list of some of the discoveries Fuller claims for
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T-to-E module transformation ("E" for "Einstein").(Fig 986.411A)
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48:(1895–1983) named and pioneered the field. His two-volume work
1359:
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R. Buckminster Fuller (in collaboration with E.J. Applewhite,
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in the form of his T&E module thread. (986.206 - 986.212)
75:, along with the posthumous naming of the carbon allotrope "
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as one of the five most formative books on sustainability.
133:
geometry of environmental forces that impact on humanity."
1080:
http://www.rwgrayprojects.com/synergetics/synergetics.html
176:
Omni-60-degree coordination versus 90-degree coordination.
950:(with permission) and by citing page 71 of the latter's
63:
Despite mainstream endorsements such as the prologue by
1377:), as two hard-bound volumes, re-editions in paperback.
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Dr. Arthur Loeb provided a prologue and an appendix to
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The Last Dymaxion: Buckminster Fuller’s Dream Restored
1355:, online edition hosted by R. W. Gray with permission
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Synergetics: Explorations in the Geometry of Thinking
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spherical triangles and their related chord factors.
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Synergetics: Explorations in the Geometry of Thinking
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60:features as Fuller's model of the simplest system.
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1098:. Carbondale and Edwardsville. pp. 118–163.
2094:R. Buckminster Fuller and Anne Hewlett Dome Home
1410:Synergetics at the Buckminster Fuller Institute
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1430:
1305:Computers & Mathematics with Applications
8:
1445:Subfields of and cyberneticians involved in
27:Empirical study of systems in transformation
1327:Hugh Kenner. The Pound Era. ISBN 0520024273
1221:12 degrees of Freedom, Ph.D. Thesis, p. xiv
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1118:: CS1 maint: location missing publisher (
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1271:Fuller, Buckminster (October 20, 1975).
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278:{\displaystyle {\sqrt {2}}\phi ^{-3}/8}
111:Fuller defined synergetics as follows:
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2122:Buckminster Fuller: Thinking Out Loud
1397:Complete On-Line Edition of Fuller's
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481:{\displaystyle 5{\sqrt {2}}\phi ^{2}}
7:
1934:Operating Manual for Spaceship Earth
1358:, originally published by Macmillan
974:Operating Manual for Spaceship Earth
433:space-filler, dual to cuboctahedron
95:(World Game). His chief assistants
67:, and positive dust cover blurbs by
1199:. Boston: Birkhauser. pp. ix.
775:Concentric Hierarchy of Polyhedrons
1405:Synergetics on the Web by K. Urner
25:
2079:Proposed Brooklyn Dodgers stadium
1285:from the original on 2021-12-20.
1136:, p. 6. Retrieved on 2010-01-26.
411:radius = ~0.9994, vol. = 120 Ts
400:dual of cube, spacefills w/ tet
1516:Cybernetics in the Soviet Union
1165:Nystrom, J. F. (October 1999).
1094:Fuller, R. Buckminster (1963).
208:
2019:Expo 67 United States Pavilion
1273:"Vector equilibrium jitterbug"
1004:: either the concept of whole
1:
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91:(New Alchemy Institute), and
2116:Buckminster Fuller Challenge
2089:Old Man River's City project
2064:Cloud Nine tensegrity sphere
1314:10.1016/0898-1221(89)90160-0
378:edges 1/2, vol. = 1/8 of 20
325:{\displaystyle \phi ^{-5}/2}
490:edges 1 = tetrahedron edge
170:The A and B Quanta Modules.
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1496:Computational neuroscience
1386:, EmergentWorld LLC, 2007.
1307:. 17, 1–3 (1–3): 203–250.
1195:Edmondson, Amy C. (1987).
512:2-frequency, 8 x 3 volume
422:radius = 1, vol. = 120 Es
367:space filling oblate octa
29:
2150:
2052:Design science revolution
1977:Dymaxion deployment unit
1669:Charles Geoffrey Vickers
1556:Second-order cybernetics
676:Rhombic Triacontahedron
438:Rhombic Triacontahedron
416:Rhombic Triacontahedron
405:Rhombic Triacontahedron
204:jitterbug transformation
140:again quoting directly:
1926:Nine Chains to the Moon
1531:Engineering cybernetics
1461:Artificial intelligence
1369:), and Vol. 2 in 1979 (
1299:Verheyen, H.F. (1989).
356:self dual, unit volume
345:space-filler, 2As + 1B
160:when referenced to the
154:rhombic triacontahedron
1854:Walter Bradford Cannon
1744:Ludwig von Bertalanffy
1599:Alfred Radcliffe-Brown
1546:Management cybernetics
1471:Biomedical cybernetics
1466:Biological cybernetics
1096:No More Secondhand God
1000:Synergetics refers to
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857:Starting with Universe
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193:Tetrahedral accounting
127:No More Secondhand God
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2036:Allegra Fuller Snyder
1814:Anthony Stafford Beer
1649:Ernst von Glasersfeld
1057:Trilinear coordinates
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693:Rhombic Dodecahedron
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444:radius = phi/sqrt(2)
427:Rhombic Dodecahedron
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46:R. Buckminster Fuller
2109:Buckminsterfullerene
2042:Current solar income
1844:Valentin Braitenberg
1724:Jay Wright Forrester
1383:A Fuller Explanation
753:Whole number volumes
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298:
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164:as volumetric unity.
158:rhombic dodecahedron
77:buckminsterfullerene
30:For other uses, see
1949:Dymaxion Chronofile
1869:William Grey Walter
1809:Sergei P. Kurdyumov
1769:N. Katherine Hayles
1551:Medical cybernetics
1511:Conversation theory
1037:Quadray coordinates
938:Academic acceptance
501:edges 1, radii = 1
233:tetrahedral voxels
2191:Buckminster Fuller
2133:(2012 documentary)
2125:(1996 documentary)
1911:Buckminster Fuller
1849:William Ross Ashby
1774:Natalia Bekhtereva
1749:Maleyka Abbaszadeh
1689:Heinz von Foerster
1614:Buckminster Fuller
1541:Information theory
1491:Catastrophe theory
884:Intuitive geometry
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334:tetrahedral voxel
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287:tetrahedral voxel
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120:Other passages in
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1799:Ranulph Glanville
1714:Jakob von Uexküll
1694:Humberto Maturana
1654:Francis Heylighen
952:Regular Polytopes
919:Social commentary
764:A & B modules
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16:(Redirected from
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1839:Valentin Turchin
1789:Pyotr Grigorenko
1734:John N. Warfield
1659:Francisco Varela
1619:Charles François
1589:Alexander Lerner
1566:Sociocybernetics
1486:Neurocybernetics
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1998:
1992:
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1980:
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1951:
1946:
1938:
1930:
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1824:Stuart Umpleby
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1796:
1791:
1786:
1784:Norbert Wiener
1781:
1779:Niklas Luhmann
1776:
1771:
1766:
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1754:Manfred Clynes
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1624:Genevieve Bell
1621:
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1611:
1609:Anthony Wilden
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1596:
1591:
1585:
1583:
1581:Cyberneticians
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1561:Cybersemiotics
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1506:Control theory
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1391:External links
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1247:Edmondson 1987
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948:H.S.M. Coxeter
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87:(tensegrity),
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1942:Critical Path
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1501:Connectionism
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1367:0-02-541870-X
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1184:200.01-203.07
1181:
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1135:
1132:CJ Fearnley,
1129:
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1105:0-8093-0247-0
1101:
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1032:Geodesic dome
1030:
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1019:
1015:
1013:
1011:
1007:
1003:
996:About synergy
995:
993:
991:
990:Synergetics 2
987:
986:Synergetics 1
979:
977:
975:
971:
967:
966:The Pound Era
962:
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642:Duo-Tet Cube
641:
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636:
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627:
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619:
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531:
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511:
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489:
473:
469:
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458:
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418:
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410:
407:
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403:
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392:
388:
385:
383:Duo-Tet Cube
382:
381:
377:
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371:
370:
366:
363:
360:
359:
355:
352:
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344:
341:
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309:
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294:
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272:
268:
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192:
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155:
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147:
143:
142:
141:
139:
134:
130:
128:
123:
117:
112:
106:
104:
102:
101:Stafford Beer
98:
97:Amy Edmondson
94:
90:
86:
80:
78:
74:
70:
66:
61:
59:
53:
51:
47:
43:
39:
33:
19:
2128:
2120:
2046:
1983:Dymaxion map
1971:Dymaxion car
1940:
1932:
1924:
1859:Walter Pitts
1764:Marian Mazur
1639:Cliff Joslyn
1481:Biosemiotics
1398:
1382:
1350:
1332:
1323:
1304:
1276:
1266:
1254:
1242:
1231:
1227:
1215:
1196:
1190:
1179:
1175:
1160:
1150:
1141:
1128:
1095:
1075:
1071:
999:
989:
985:
983:
973:
969:
965:
963:
958:
956:
951:
943:
941:
932:
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913:
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906:
902:
898:
894:
890:
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874:
865:
860:
847:
834:
829:
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816:
811:
802:
798:
790:
778:
767:
756:
608:Tetrahedron
449:Icosahedron
350:Tetrahedron
196:
187:
184:Significance
137:
135:
131:
126:
121:
119:
114:
110:
93:Medard Gabel
81:
62:
54:
49:
37:
36:
2186:Cybernetics
2047:Synergetics
2007:Octet truss
1794:Qian Xuesen
1674:Gordon Pask
1571:Synergetics
1536:Homeostasis
1476:Biorobotics
1447:cybernetics
1399:Synergetics
1232:Synergetics
1180:Synergetics
1155:University)
1076:Synergetics
1052:Tetrahedron
1042:Octet Truss
959:Synergetics
944:Synergetics
924:Synergetics
781:Fig. 990.01
659:Octahedron
394:Octahedron
222:Properties
199:tetrahedron
162:tetrahedron
138:Synergetics
122:Synergetics
65:Arthur Loeb
58:tetrahedron
38:Synergetics
32:Synergetics
2175:Categories
2038:(daughter)
2001:World Game
1989:Tensegrity
1375:0025418807
1344:References
1249:, pp. ix-x
1047:Tensegrity
1022:Cloud Nine
1010:negentropy
156:, and the
146:octahedron
107:Definition
89:J. Baldwin
18:Synergetic
2104:Fullerene
2084:Gold Dome
1526:Emergence
1454:Subfields
1114:cite book
574:T module
557:B module
540:A module
470:ϕ
389:24 MITEs
307:−
303:ϕ
292:S module
260:−
256:ϕ
238:E module
42:empirical
2155:Category
2074:Dymaxion
2069:Geoscope
1283:Archived
1261:, p. xiv
1016:See also
972:circled
727:2F Cube
625:Coupler
506:2F Cube
361:Coupler
2160:Commons
2029:Related
1278:YouTube
1234:, Sec.
1182:, Sec.
1002:synergy
842:527.712
838:527.702
820:986.203
806:1075.11
793:1071.10
526:Volume
219:Volume
69:U Thant
40:is the
2181:Holism
2021:(1967)
2015:(1965)
2009:(1961)
2003:(1961)
1997:(1953)
1991:(1949)
1985:(1946)
1979:(1940)
1973:(1933)
1967:(1928)
1945:(1981)
1937:(1968)
1929:(1938)
1373:
1365:
1236:251.50
1203:
1102:
1006:system
980:Errata
970:Nature
869:307.04
851:250.30
785:528.00
523:Shape
216:Shape
152:, the
148:, the
1958:Other
1918:Books
1259:Clark
1063:Notes
591:MITE
577:1/24
560:1/24
543:1/24
339:MITE
230:1/24
1371:ISBN
1363:ISBN
1201:ISBN
1120:link
1100:ISBN
736:192
733:384
719:144
716:336
688:120
594:1/8
441:7.5
375:2.5
342:1/8
150:cube
71:and
1309:doi
946:to
730:24
713:20
702:48
699:96
668:48
665:48
651:24
648:48
631:16
614:24
509:24
498:20
419:5+
2177::
1303:.
1291:^
1281:.
1275:.
1116:}}
1112:{{
1086:^
1078:,
1012:.
871:)
853:)
844:)
840:,
822:)
808:)
795:)
739:0
722:0
705:0
696:6
685:0
682:0
679:5
671:0
662:4
654:0
645:3
637:0
634:8
628:1
620:0
617:0
611:1
603:0
600:1
597:2
586:1
583:0
580:0
569:0
566:1
563:0
552:0
549:0
546:1
535:T
532:B
529:A
430:6
408:5
397:4
386:3
364:1
353:1
206:.
129:.
1903:e
1896:t
1889:v
1438:e
1431:t
1424:v
1317:.
1311::
1209:.
1122:)
1108:.
849:(
818:(
474:2
464:2
459:5
320:2
316:/
310:5
273:8
269:/
263:3
250:2
34:.
20:)
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