Index and Glossary
1This is both an index and a glossary. The definitions provided are consistent with Fuller’s perceptions. For more on the geometrical terms, see Fuller’s Synergetics and Synergetics 2, which provide comprehensive explanations of his synergetic geometry. For more on Fuller’s thinking about humanity, see Critical Path and Crunch of Giants.
2 When a word within a definition appears in italics, refer to that word’s separate entry in this index/glossary for a definition. Italicized page numbers signify illustrations.
3 A
4 Advantage Power of a lever, 53
5 Afghanistan, 132
6 Alloys, 13
7 Allspace filling A system that, when repeated, fills all space, leaving no space unfilled. 80
8 Angle The shape resulting from the intersection of two lines or surfaces.
9 ---as hinge, 50
10 Animate, 140-141
11 Archimedes, 54
12 Area The face or window of a. system. 61
13 Axis The imaginary line at the center of a rotating object around which the object rotates.
14 ---Earth’s, 31
15 B
16 Belief A hand-me-down claim to ‘‘reality,’’ personally untested and potentially unfounded (versus knowing). 17, 18, 113--114
17 Between-ness The property of relationship shared by two points. 60 Boole, George, 44
1819Brain The organ that coordinates and differentiates information from the five physical senses; the brain deals only with special-case (instance by instance) information, as distinguished from mind. 126-128
20 ---deals in temporals, 127
2122C
23 Cambodia, 133
2425Center (see Nucleus), 34--36,69--70074--7777, 783--84-84, 104, 123 Children
26---as spontaneously self-directed and trustworthy beings, 24 ---development of, 125--126, 132
27 Chromosomes, 140
2829Comprehensivism Dedication to perceiving relationships between all areas of human experience, relying on the scientific method and rejecting mere belief. 20, 138
30Compression In architecture, building using earthward pressure; as opposed to tension. 94 ---limit to cross-section in compressional structures, 97
31 Concepts
32 ---independent of size, 81
3334Convergence Coming together toward a common center. 67, 103-104
35 Copernican Revolution, 127
36 Copernicus, Nicolaus Fn. 127
37 Corners The vertexes of a system. 61, 62
38 Cousins, Norman
39 ---Foreword, ix
4041Cube An unstable structure of eight corners and six areas. 62, 81, ---as having only three faces, 72 ---formed from ‘‘cut’’ octahedron, 84 ---stabilized by tetrahedron, 62-63 ---star tetrahedron as only real cube, 64 ---as three dimensional, 72 ---triangulated cube, 63
42Cubing Inaccurate term for increasing the volume of a system by doubling the length of exterior edges. See tetrahedroning. 86-91
43D
44 Dacron, 44
45 Da Vinci, Leonardo, 23
46 Death
47 ---unreality of, 140-141
4849Degree A ‘/jmjM division of a circle, used as the basic unit for measuring angles.
50 Distribution of resources
51 ---as basic challenge facing humanity, 110
5253Divergence Moving farther and farther apart outwardly from a common center. 67, 103-104 ---and evolution, 123
54 DNA, 140
55 Doubling of volume
56 ---effects on cube and tetrahedron, 81-82
57 Down Erroneous term; see in. 103-104
5859E
60‘‘Earning a living’’ Fallacious and dangerous human belief that humans have no inherent right to exist and must therefore ‘‘earn’’ it. 21-22,110,134-135
61 Economy
62 ---basis of future, 135
6364Edges The margins (lines) defining of the windows (areas, faces) of a system, which appear to intersect at the ’vertexes (corners). 61 ---six edges as minimum for system, 93
65 Edison, Thomas Alva, 109
66 Education
67 ---in future, 109
68 ---ideal form, 125-126, 132
69 Einstein, Albert
70 ---and curved space, 43
71 ---and non-instantaneous universe, 118-121
72 El Salvador, 133
73 Energy crisis
74 ---unreality of, 136
75 Ephemeralization The process of doing more with less. 21
76 Equator An imaginary great circle on the earth’s surface exactly midway at all points between the North and South Poles. 31 ---as great circle, 34
77 Euler, Leonhard, 61
78 Euler’s Law The number of corners of any polyhedron added to the number of areas (windows, faces’) always equals the number of edges plus the number 2. 62 ---and the octahedron, 79
79 ---and the vector equilibrium, 77-79
80 Existence
81 ---qualities of, 41
82 Experimental evidence, 49
83 F
84 Face An area or window of a system. 62
85 Fail-safe circuits, 114
86 Favoritism, 129
87 Four
88 ---as minimum number for reality, 60
89 Frequency The number of times an event occurs in a unit of time or space. 48-49
90 ---of vector equilibrium, 78-79
91 Fulcrum Base (pivot point) of a lever. 53
92 Fuller, Alexandra, 15-16, 114
93 Fuller, Allegra (Snyder), 5
94 Fuller, Anne Hewlett, 5,114, 141
95 Fuller, Margaret, 4
96 Fuller, Richard Buckminster
97 ---and children, 157-159
98 ---death, 141
99 ---educational experiences, 12-13, 27-28, 133, 138
100 ---as exemplar, 24
101 ---family heritage, 12
102 ---favorite childhood stories, 138
103 ---feelings on completing projects, 130
104 ---first thoughts, 107-108
105 ---Harvard experience, 12-13
106 ---hopes for own works, 135-136
107 ---life experiment, 22-23
108 ---as machinist, 12-13
109 ---naval experience, 13-15
110 ---relations with collaborators, 134-135
111 ---religious creed, 18-19, 22-23
112 ---sleep patterns, 130-131
113 ---suicide plans, 11-23
114 ---treatment by schoolmates, 109
115 ---and Woodrow Wilson, 14
116117G
118 Generalizaton
119 ---as convergence, 123
120 Genes, 140
121 Geodesic domes
122 ---based on icosahedron, 94
123 ---efficiency of, 123-125
124 ---in space, 116
125 Geometry
126 ---traditionally defined, 28
127 ---synergetic, 64
128 God, 18, 23
129 ---as Greater Intellectual Integrity, 18, 19, 22-23, 115-116, 136
130 Good and bad, 115
131 Government
132 ---ideal form, 111-113
133 Gravity, 127
134 Great Circle: Any line on the surface of a sphere describing a plane running through the center of the sphere, dividing it into two hemispheres. 34-35
135 ---as navigation aid, 37
136137H
138 Haldane, J. B. S., 22
139 Hemisphere Literally, half a sphere; either of the two halves of the earth formed by a great circle. 32
140 Heroes, 129
141 Hexagon (regular) A polygon formed of six equal edges and six equal angles.
142 ---as formed by closest-packed spheres, 69-70
143 Hinges
144 ---instability of, 50
145 ---triangles as restrained hinges, 52
146 Historical events
147 ---most important recent, 137-138
148 Housing
149 ---use of technology for, 97
150 Humans
151 ---emergence as world people, 137
152 ---function of, 122, 136
153 ---least specialized beings in nature, 123
154155I
156 Icosahedron A 20-sided geometric structure with five triangular faces meeting at every vertex. 92, 93 ---as basis of geodesic domes, 94 ---as basis of accurate maps, 100-102
157 Imaginary numbers
158 ---as products of erroneous cubic-based geometry, 91
159 Importance, relative
160 ---of various cultures, 129
161 In Convergent motion toward a common center; replaces erroneous term down. 103
162 Inanimate, 140-141
163 Infinity The erroneous assumption that Universe is boundless, and therefore unfathomable.
164 ---as imaginary concept, 29-31
165 Inside
166 ---as element of systems, 33, 41
167168K
169 Knowledge, 17
170171L
172 Latitude The angle of a point on the earth’s surface as measured in degrees along a meridian north or south from the center of the plane of the Equator. 35, 3 6
173 Laws Scientifically verified statements describing omni-occurring relationships between specific conditions (givens) and their invariable outcomes. 18, 127
174 Lesser circle Any circle drawn on the surface of a sphere that does not describe a plane passing through the center of the sphere. See great circle. 35, 37
175 Lever
176 ---defined, 53, 53
177 Life , 1 ~
178 ---extraterrestrial, 116
179 ---function of intelligent life, 116
180 ---as ‘‘inventory of experiences’ ’, 18
181 ---invisible forms, 139
182 ---not physical, 139
183 ---weightless, 140-141
184 Lindbergh, Charles Augustus, 11
185 Line Traditionally defined as the shortest distance between any two points; but described by Fuller as a ‘‘wavilinear’ ’ (wave) form produced by the interaction of all the motions operating on an event; an event having reality as the edge of a system.
186 ---as edge of system, 62
187 ---deliberately non-straight line, 44-49
188 ---straight lines unreal, 29-32, 42, 49, 113
189 ---as history, 49
190 ---traditionally defined, 29
191 ---of latitude, 35
192 ---of longitude, 34
193 ---of sight, 42
194 ---wave lines, 49
195 Livingry Technology applied for purposes of helping humanity succeed. 20
196 Loci ‘‘Corners’ ’ (crossings, or vertexes) of a system. 61
197 Longitude A geographical term for a great circle meridian, measured from a meridian passing through the Royal Observatory at Greenwich, England. 34
198 Love, 19
199 M
200 Mack, Art, 6
201 Mack, Benjamin, 6
202 ---on Fuller’s death, 141
203 ---Fuller’s response to, 158
204 ---perceptions of Fuller, 149
205 ---and synergetic modeling, 159
206207---questions from, 107, 108, 109-110, 113, 115, 121, 126, 129, 130, 132, 133, 134, 135, 136, 137, 138, 139
208 Mack, Lucy, 6
209210Macrocosm That part of the universe contained within a given system. 66
211 Maps, 98-102
212 Marxism, 21
213 Mercator projection Inaccurate map. 98-99
214215Meridian A great circle passing through both the earth’s poles; a meridian of longitude. 34
216 Microcosm That part of the universe outside a given system. 66
217218Mind The ability of humans to discover relationships between the special-case data perceived by brain. 126-128, 136 ---focus on externals, 127
219 ---like television director, 127-128
220 Minimum numbers, 61
221 Minimum something, 61
222 Mistakes
223 ---vital elements in learning, 113
224 Myrow, Fredric, 6
225 Myrow, Iliana, 6
226 Myrow, Rachel, 6
227 ----Fuller’s response to, 158
228 ---perceptions of Fuller, 152-153
229230---questions from, 107, 111, 117, 125, 130, 131, 133, 134, 135, 139
231N
232 Nature
233 ---checks and balances of, 121
234 ---and function, 121
235 Nesmith, Jonathan, 6
236 ---Fuller’s response to, 158
237 ---perceptions of Fuller, 145-148
238 ---questions from, 109, 110, 115, 116, 117, 122, 123, 128, 138
239 Nesmith, Michael, 6
240 Nesmith, Phyllis, 6
241 Nicaragua, 133
242243North Pole The northern end of the axis on which the earth rotates., 31, 36
244Nucleus The central element of a structure around which other elements arc arrayed in triangulated (synergetic) symmetry and which provides a fulcrum for the understanding. 70
245 O
246247Octahedron Triangulated system of eight equal areas, six vertexes, and twelve edges. 79
248Octet truss A structure composed entirely of octahedrons and tetrahedrons that work together to fill all space, leaving nothing unfilled. 80 ---volume multiplied by tetrahedroning, 87-90
249Out Motion diverging from a common center; replaces erroneous term up. 103
250 Outsidedness
251 ---as element of systems, 33, 41
252 ---as single-frame picture, 120
253 P
254255Parallel An outmoded concept based on the belief that two lines can extend to infinity without touching. 67, 103
256Perpendicular The erroneous concept that major relationships in universe are at 90°angles to each other. 67, 103
257Photosynthesis The use of solar energy by plants to turn water, chemicals, and gases into nutrients. 121
258Plane Traditionally, an imaginary flat area reaching out to infinity and containing all the straight lines connecting any two points on it; an event that never occurs in universe. 28
259 ---flatness proven unreal, 40
260261Point An imaginary, therefore unreal, event consisting of no dimensionality yet somehow having location. 41, 50-60
262Pole The point at which the axis of rotation of a sphere meets the surface of the sphere. 31
263 Politics
264 ---irrelevance of, 109
265266Polygon An imaginary figure described by connected lines on a plane. 50
267 Polyhedron A system with several surfaces. 41
268 ---and Euler’s Law, 62
269 Population
270 ---relative concentration, 102 17[-
271 Population explosion, 121, 122
272 Principles
273 ---independent of size, 79
274 Problems, 134, 135
275 ---Fuller’s approach to solving
276 Problems of future, 131-132
277 ---need for accurate mathematical coordinate system, 132
278 Push-pull Any side opposite any angle in a triangle; the source of the triangle’s stability. 54
279280R
281 Reading, recommended, 138-139
282 Reality
283 ---99.9 percent invisible to senses, 132
284 Recreation
285 ---activities of future, 128-129
286 Reduction from absurdity, 44
287 Reflexing
288 ---different from thinking, 108
289 Relationships, 41
290 Rhombus A geometrical shape of four equal edges and two pairs of angles, the members of each pair equal to themselves and complementary to the members of the other pair. 46
291 RNA, 140
292 Robin Hood, 138
293 Russia, 132, 133
294295S
296 Satellites
297 ---use in future government, 111-112
298 Schools
299 ---alternatives to, 107, 109
300 ---as sources of oversimplification, 33
301 Science The use of mind to discover generalized laws. 127
302 Scissors
303 ---as paired levers, 54
304 Seeability The quality of being visible to the human sensory apparatus (eyes).
305 ---elements of, 61
306 Servomechanisms, 113
307 Shortages of life support Illusory belief that the earth lacks enough resources to meet human survival needs. 21-22
308 Sides Erroneous concept for the windows or faces of a system. 61
309 Six
310 ---as beginning of structural system, 93
311 Sleep, 130-131
312 Snyder, Jaime, 5
313 Socialism, 133
314 Social Darwinism, 21
315 ‘‘Something’’ An entity {system) having existence in the real world.
316 60-61
317 South Pole See North Pole. 31, 36
318 Space
319 ---curved, 43
320 Spaceship Earth, 14, 15, 20, 24, 103-104, 160
321 Space Travel, 117
322 Specialization
323 ---as divergence, 122-123
324 ---fostered by power elites, 132
325 Sphere A geometrical structure in which all surface points are equidistant from a common center. 68 ---closest-packed spheres, 68
326 Sphere of rotation, 65
327 Spherical trigonometry The study of triangles formed on the surfaces of spheres. 37-38
328 Square An imaginary geometric construct consisting of four equal sides and four right (90°) angles.
329 ---formed by octahedron, 83
330 ---not a structure, 56
331 ---stabilized by triangles, 52, 58
332 ---traditionally defined, 28
333 ---unreality of, 50
334 Squaring Redefined as ‘‘triangling.’’ 56-58
335 Stars
336 ---as energy events, 119
337 ---relative distances, 118-119
338 Structure A complex of events that interact to form a stable pattern.
339 55, 56
340 ---tetrahedron as structure, 61
341 ---size and energy efficiency, 124
342 Sunclipse Accurate term for last sighting of the sun at western horizon as the segment of earth on which the observer stands rotates away from the sun. 102
343 Sunrise Erroneous term based on false perception of the sun’s relationship to earth; see sunsight. 102
344 Sunset See sunrise. 102
345 Sunsight Accurate term for first sighting of the sun at the eastern horizon as the segment of earth on which the observer stands rotates toward the sun. 102
346 Surface An element of a system having no independent existence outside the system. 60
347 System Triangularly based structures that divide universe into an in- sidedness, an outsidedness, and the system itself. 66 ---all systems ‘‘closed’’, 32
348 T
349 Teachers
350 ---as sources of misinformation, 27-28
351 Telepathy
352 ---as electromagnetic wave phenomenon, 112, 114-115
353 ---and world government, 112-113
354 ---reality of, 113-115
355 Television
356 ---two-way use in education, 109
357 Temperature
358 ---variations on earth, 100-101
359 Tension In architecture, employing outwardly stretching forces to impart structural stability. 95
360 Tensional integrity, or tensegrity A structure employing equally distributed tension to hold islands of compression in stability. 95,96 ---no limit to cross-section in tensegrity structures, 98
361 Tetrahedron The minimum structure of Universe, composed of four windows (faces) formed by six edges intersecting at four corners (vertexes). 60, 63 ---as electron, 91
362 ---formed by closest-packed spheres, 68
363 ---as four-dimensional, 72
364 ---star tetrahedron, 64
365 ---as quantum, 91
366 Tetrahedroning Nature’s way of increasing volumes geometrically, erroneously called cubing. 86-91
367 Thought
368 ---as convergent and divergent, 67
369 ---different from reftexing, 108
370 ---function of mind, not brain, 127
371 Three
372 ---properties of ‘‘threencss,’’ 60
373 Triangle A polygon formed by the intersection of three lines, having three angles, and possessed of stability because each angle is held in place by an opposite push-pull; the only stable polygon and the basis of all synergetic geometry.
374 ---efficiency of, 58
375 ---elements of, 55
376 ---equilateral, 28-29
377 ---independent of size, 79
378 ---as only real shape, 52
379 ---as restrained hinge, 52
380 ---traditionally defined, 28
381 ---spherical, 52-41
382 ---spherical equilateral, 40
383 ---stability of, 50-52, 58
384 Triangling Multiplying a unit of measure by itself; traditionally called squaring. 56-59
385 Trigonometry The study of the relationships of lines and angles in the triangle. 37-38
386 Tuning The process of establishing the desired frequency of a system.
387 66
388 Two
389 ---properties of ‘‘twoness,’’ 60
390 U
391 Understanding The process by which the mind discovers relationships. 125
392 United States, 133
393 Universe The sum total of humanity’s consciously apprehended and communicated experience. 117-121 ---non-instantaneous, 117-120 ---as scenario, 119-121
394 Up Erroneous term, see out. 103-104
395 Vector equilibrium The structure formed by closest-packing of one layer of spheres around a nucleus; having eight square and six triangular faces, with each vertex equidistant from the center. ---and atomic physics, 79 ---and Euler’s Law, 77 ---expanded in frequency, 76-79 ---as formed by closest-packed spheres, 70-72 ---frequencies of, 78-79 ---as model of atomic packing, 74
396 ---as sharing the planes of the tetrahedron, 72-74
397 ---planes of, 74
398 ---modeled from paper circles, 75-76
399 Vegetation
400 ---function of, 121
401 Verkhoyansk, 100
402 Vertex The corner of a system, formed by the convergence of lines or edges. 62
403 ---three triangles meet at vertexes of tetrahedron, 91
404 ---four triangles meet at vertexes of octahedron, 91
405 ---five triangles meet at vertexes of icosahedron, 91
406 Volume The extent of space enclosed by geometric structures.
407 ---of tetrahedrons, 81
408 ---increased by tetrahedroning, 91
409 ---of octahedrons, 84
410 ---of cubes, 85
411412W
413 War
414 ---dangers of, 132-133, 135
415 Wave The pattern of motion produced by the transfer of energy through a medium. 48-49
416 Wavilinearity The property of all lines, which are always and inherently formed by wave motion.
417 ---nature operates through
418 Wilson, Woodrow, 14
419 Window The faces (areas or openings) of a system. 61
420(continued from front flap)
421 Here is Bucky explaining step-by-step how the universe works, with interruptions by the kids any time they couldn’t follow him or weren’t quite sure what he meant, along with sketches Bucky used to explain things and photographs of all four intently in conversation. In the follow-up session the kids were allowed to ask him any questions they wanted---some quite personal---and the resulting discussion sparkles with the delight of young minds opening---‘‘Boy, is that neat!’’---and presents a living portrait of one of the great minds of the twentieth century at work.
422 For anyone interested in this remarkable man or in the most direct and elementary exposition of his philosophy available, this book will be invaluable---as well as a sheer delight to read.
423Richard J. Brenneman, an award-winning journalist for the Sacramento Bee, has followed Buckminster Fuller’s career for fifteen years. He lives with his wife and two children in Davis, California.
424Jacket photo by Richard J. Brenneman
425Jacket by Manuela Paul
426 St. Martins Press 175 Fifth Avenue New York, N.Y. 10010
427 PRINTED IN THE U.S.A.