Index and Glossary
2This 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.
3 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.
4 A
5 Advantage Power of a lever, 53
6 Afghanistan, 132
7 Alloys, 13
8 Allspace filling A system that, when repeated, fills all space, leaving no space unfilled. 80
9 Angle The shape resulting from the intersection of two lines or surfaces.
10 ---as hinge, 50
11 Animate, 140-141
12 Archimedes, 54
13 Area The face or window of a. system. 61
14 Axis The imaginary line at the center of a rotating object around which the object rotates.
15 ---Earth’s, 31
16 B
17 Belief A hand-me-down claim to ‘‘reality,’’ personally untested and potentially unfounded (versus knowing). 17, 18, 113--114
18 Between-ness The property of relationship shared by two points. 60 Boole, George, 44
1920Brain 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
21 ---deals in temporals, 127
2223C
24 Cambodia, 133
2526Center (see Nucleus), 34--36,69--70074--7777, 783--84-84, 104, 123 Children
27---as spontaneously self-directed and trustworthy beings, 24 ---development of, 125--126, 132
28 Chromosomes, 140
2930Comprehensivism Dedication to perceiving relationships between all areas of human experience, relying on the scientific method and rejecting mere belief. 20, 138
31Compression In architecture, building using earthward pressure; as opposed to tension. 94 ---limit to cross-section in compressional structures, 97
32 Concepts
33 ---independent of size, 81
3435Convergence Coming together toward a common center. 67, 103-104
36 Copernican Revolution, 127
37 Copernicus, Nicolaus Fn. 127
38 Corners The vertexes of a system. 61, 62
39 Cousins, Norman
40 ---Foreword, ix
4142Cube 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
43Cubing Inaccurate term for increasing the volume of a system by doubling the length of exterior edges. See tetrahedroning. 86-91
44D
45 Dacron, 44
46 Da Vinci, Leonardo, 23
47 Death
48 ---unreality of, 140-141
4950Degree A ‘/jmjM division of a circle, used as the basic unit for measuring angles.
51 Distribution of resources
52 ---as basic challenge facing humanity, 110
5354Divergence Moving farther and farther apart outwardly from a common center. 67, 103-104 ---and evolution, 123
55 DNA, 140
56 Doubling of volume
57 ---effects on cube and tetrahedron, 81-82
58 Down Erroneous term; see in. 103-104
5960E
61‘‘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
62 Economy
63 ---basis of future, 135
6465Edges 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
66 Edison, Thomas Alva, 109
67 Education
68 ---in future, 109
69 ---ideal form, 125-126, 132
70 Einstein, Albert
71 ---and curved space, 43
72 ---and non-instantaneous universe, 118-121
73 El Salvador, 133
74 Energy crisis
75 ---unreality of, 136
76 Ephemeralization The process of doing more with less. 21
77 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
78 Euler, Leonhard, 61
79 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
80 ---and the vector equilibrium, 77-79
81 Existence
82 ---qualities of, 41
83 Experimental evidence, 49
84 F
85 Face An area or window of a system. 62
86 Fail-safe circuits, 114
87 Favoritism, 129
88 Four
89 ---as minimum number for reality, 60
90 Frequency The number of times an event occurs in a unit of time or space. 48-49
91 ---of vector equilibrium, 78-79
92 Fulcrum Base (pivot point) of a lever. 53
93 Fuller, Alexandra, 15-16, 114
94 Fuller, Allegra (Snyder), 5
95 Fuller, Anne Hewlett, 5,114, 141
96 Fuller, Margaret, 4
97 Fuller, Richard Buckminster
98 ---and children, 157-159
99 ---death, 141
100 ---educational experiences, 12-13, 27-28, 133, 138
101 ---as exemplar, 24
102 ---family heritage, 12
103 ---favorite childhood stories, 138
104 ---feelings on completing projects, 130
105 ---first thoughts, 107-108
106 ---Harvard experience, 12-13
107 ---hopes for own works, 135-136
108 ---life experiment, 22-23
109 ---as machinist, 12-13
110 ---naval experience, 13-15
111 ---relations with collaborators, 134-135
112 ---religious creed, 18-19, 22-23
113 ---sleep patterns, 130-131
114 ---suicide plans, 11-23
115 ---treatment by schoolmates, 109
116 ---and Woodrow Wilson, 14
117118G
119 Generalizaton
120 ---as convergence, 123
121 Genes, 140
122 Geodesic domes
123 ---based on icosahedron, 94
124 ---efficiency of, 123-125
125 ---in space, 116
126 Geometry
127 ---traditionally defined, 28
128 ---synergetic, 64
129 God, 18, 23
130 ---as Greater Intellectual Integrity, 18, 19, 22-23, 115-116, 136
131 Good and bad, 115
132 Government
133 ---ideal form, 111-113
134 Gravity, 127
135 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
136 ---as navigation aid, 37
137138H
139 Haldane, J. B. S., 22
140 Hemisphere Literally, half a sphere; either of the two halves of the earth formed by a great circle. 32
141 Heroes, 129
142 Hexagon (regular) A polygon formed of six equal edges and six equal angles.
143 ---as formed by closest-packed spheres, 69-70
144 Hinges
145 ---instability of, 50
146 ---triangles as restrained hinges, 52
147 Historical events
148 ---most important recent, 137-138
149 Housing
150 ---use of technology for, 97
151 Humans
152 ---emergence as world people, 137
153 ---function of, 122, 136
154 ---least specialized beings in nature, 123
155156I
157 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
158 Imaginary numbers
159 ---as products of erroneous cubic-based geometry, 91
160 Importance, relative
161 ---of various cultures, 129
162 In Convergent motion toward a common center; replaces erroneous term down. 103
163 Inanimate, 140-141
164 Infinity The erroneous assumption that Universe is boundless, and therefore unfathomable.
165 ---as imaginary concept, 29-31
166 Inside
167 ---as element of systems, 33, 41
168169K
170 Knowledge, 17
171172L
173 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
174 Laws Scientifically verified statements describing omni-occurring relationships between specific conditions (givens) and their invariable outcomes. 18, 127
175 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
176 Lever
177 ---defined, 53, 53
178 Life , 1 ~
179 ---extraterrestrial, 116
180 ---function of intelligent life, 116
181 ---as ‘‘inventory of experiences’ ’, 18
182 ---invisible forms, 139
183 ---not physical, 139
184 ---weightless, 140-141
185 Lindbergh, Charles Augustus, 11
186 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.
187 ---as edge of system, 62
188 ---deliberately non-straight line, 44-49
189 ---straight lines unreal, 29-32, 42, 49, 113
190 ---as history, 49
191 ---traditionally defined, 29
192 ---of latitude, 35
193 ---of longitude, 34
194 ---of sight, 42
195 ---wave lines, 49
196 Livingry Technology applied for purposes of helping humanity succeed. 20
197 Loci ‘‘Corners’ ’ (crossings, or vertexes) of a system. 61
198 Longitude A geographical term for a great circle meridian, measured from a meridian passing through the Royal Observatory at Greenwich, England. 34
199 Love, 19
200 M
201 Mack, Art, 6
202 Mack, Benjamin, 6
203 ---on Fuller’s death, 141
204 ---Fuller’s response to, 158
205 ---perceptions of Fuller, 149
206 ---and synergetic modeling, 159
207208---questions from, 107, 108, 109-110, 113, 115, 121, 126, 129, 130, 132, 133, 134, 135, 136, 137, 138, 139
209 Mack, Lucy, 6
210211Macrocosm That part of the universe contained within a given system. 66
212 Maps, 98-102
213 Marxism, 21
214 Mercator projection Inaccurate map. 98-99
215216Meridian A great circle passing through both the earth’s poles; a meridian of longitude. 34
217 Microcosm That part of the universe outside a given system. 66
218219Mind The ability of humans to discover relationships between the special-case data perceived by brain. 126-128, 136 ---focus on externals, 127
220 ---like television director, 127-128
221 Minimum numbers, 61
222 Minimum something, 61
223 Mistakes
224 ---vital elements in learning, 113
225 Myrow, Fredric, 6
226 Myrow, Iliana, 6
227 Myrow, Rachel, 6
228 ----Fuller’s response to, 158
229 ---perceptions of Fuller, 152-153
230231---questions from, 107, 111, 117, 125, 130, 131, 133, 134, 135, 139
232N
233 Nature
234 ---checks and balances of, 121
235 ---and function, 121
236 Nesmith, Jonathan, 6
237 ---Fuller’s response to, 158
238 ---perceptions of Fuller, 145-148
239 ---questions from, 109, 110, 115, 116, 117, 122, 123, 128, 138
240 Nesmith, Michael, 6
241 Nesmith, Phyllis, 6
242 Nicaragua, 133
243244North Pole The northern end of the axis on which the earth rotates., 31, 36
245Nucleus 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
246 O
247248Octahedron Triangulated system of eight equal areas, six vertexes, and twelve edges. 79
249Octet 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
250Out Motion diverging from a common center; replaces erroneous term up. 103
251 Outsidedness
252 ---as element of systems, 33, 41
253 ---as single-frame picture, 120
254 P
255256Parallel An outmoded concept based on the belief that two lines can extend to infinity without touching. 67, 103
257Perpendicular The erroneous concept that major relationships in universe are at 90°angles to each other. 67, 103
258Photosynthesis The use of solar energy by plants to turn water, chemicals, and gases into nutrients. 121
259Plane 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
260 ---flatness proven unreal, 40
261262Point An imaginary, therefore unreal, event consisting of no dimensionality yet somehow having location. 41, 50-60
263Pole The point at which the axis of rotation of a sphere meets the surface of the sphere. 31
264 Politics
265 ---irrelevance of, 109
266267Polygon An imaginary figure described by connected lines on a plane. 50
268 Polyhedron A system with several surfaces. 41
269 ---and Euler’s Law, 62
270 Population
271 ---relative concentration, 102 17[-
272 Population explosion, 121, 122
273 Principles
274 ---independent of size, 79
275 Problems, 134, 135
276 ---Fuller’s approach to solving
277 Problems of future, 131-132
278 ---need for accurate mathematical coordinate system, 132
279 Push-pull Any side opposite any angle in a triangle; the source of the triangle’s stability. 54
280281R
282 Reading, recommended, 138-139
283 Reality
284 ---99.9 percent invisible to senses, 132
285 Recreation
286 ---activities of future, 128-129
287 Reduction from absurdity, 44
288 Reflexing
289 ---different from thinking, 108
290 Relationships, 41
291 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
292 RNA, 140
293 Robin Hood, 138
294 Russia, 132, 133
295296S
297 Satellites
298 ---use in future government, 111-112
299 Schools
300 ---alternatives to, 107, 109
301 ---as sources of oversimplification, 33
302 Science The use of mind to discover generalized laws. 127
303 Scissors
304 ---as paired levers, 54
305 Seeability The quality of being visible to the human sensory apparatus (eyes).
306 ---elements of, 61
307 Servomechanisms, 113
308 Shortages of life support Illusory belief that the earth lacks enough resources to meet human survival needs. 21-22
309 Sides Erroneous concept for the windows or faces of a system. 61
310 Six
311 ---as beginning of structural system, 93
312 Sleep, 130-131
313 Snyder, Jaime, 5
314 Socialism, 133
315 Social Darwinism, 21
316 ‘‘Something’’ An entity {system) having existence in the real world.
317 60-61
318 South Pole See North Pole. 31, 36
319 Space
320 ---curved, 43
321 Spaceship Earth, 14, 15, 20, 24, 103-104, 160
322 Space Travel, 117
323 Specialization
324 ---as divergence, 122-123
325 ---fostered by power elites, 132
326 Sphere A geometrical structure in which all surface points are equidistant from a common center. 68 ---closest-packed spheres, 68
327 Sphere of rotation, 65
328 Spherical trigonometry The study of triangles formed on the surfaces of spheres. 37-38
329 Square An imaginary geometric construct consisting of four equal sides and four right (90°) angles.
330 ---formed by octahedron, 83
331 ---not a structure, 56
332 ---stabilized by triangles, 52, 58
333 ---traditionally defined, 28
334 ---unreality of, 50
335 Squaring Redefined as ‘‘triangling.’’ 56-58
336 Stars
337 ---as energy events, 119
338 ---relative distances, 118-119
339 Structure A complex of events that interact to form a stable pattern.
340 55, 56
341 ---tetrahedron as structure, 61
342 ---size and energy efficiency, 124
343 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
344 Sunrise Erroneous term based on false perception of the sun’s relationship to earth; see sunsight. 102
345 Sunset See sunrise. 102
346 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
347 Surface An element of a system having no independent existence outside the system. 60
348 System Triangularly based structures that divide universe into an in- sidedness, an outsidedness, and the system itself. 66 ---all systems ‘‘closed’’, 32
349 T
350 Teachers
351 ---as sources of misinformation, 27-28
352 Telepathy
353 ---as electromagnetic wave phenomenon, 112, 114-115
354 ---and world government, 112-113
355 ---reality of, 113-115
356 Television
357 ---two-way use in education, 109
358 Temperature
359 ---variations on earth, 100-101
360 Tension In architecture, employing outwardly stretching forces to impart structural stability. 95
361 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
362 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
363 ---formed by closest-packed spheres, 68
364 ---as four-dimensional, 72
365 ---star tetrahedron, 64
366 ---as quantum, 91
367 Tetrahedroning Nature’s way of increasing volumes geometrically, erroneously called cubing. 86-91
368 Thought
369 ---as convergent and divergent, 67
370 ---different from reftexing, 108
371 ---function of mind, not brain, 127
372 Three
373 ---properties of ‘‘threencss,’’ 60
374 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.
375 ---efficiency of, 58
376 ---elements of, 55
377 ---equilateral, 28-29
378 ---independent of size, 79
379 ---as only real shape, 52
380 ---as restrained hinge, 52
381 ---traditionally defined, 28
382 ---spherical, 52-41
383 ---spherical equilateral, 40
384 ---stability of, 50-52, 58
385 Triangling Multiplying a unit of measure by itself; traditionally called squaring. 56-59
386 Trigonometry The study of the relationships of lines and angles in the triangle. 37-38
387 Tuning The process of establishing the desired frequency of a system.
388 66
389 Two
390 ---properties of ‘‘twoness,’’ 60
391 U
392 Understanding The process by which the mind discovers relationships. 125
393 United States, 133
394 Universe The sum total of humanity’s consciously apprehended and communicated experience. 117-121 ---non-instantaneous, 117-120 ---as scenario, 119-121
395 Up Erroneous term, see out. 103-104
396 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
397 ---as sharing the planes of the tetrahedron, 72-74
398 ---planes of, 74
399 ---modeled from paper circles, 75-76
400 Vegetation
401 ---function of, 121
402 Verkhoyansk, 100
403 Vertex The corner of a system, formed by the convergence of lines or edges. 62
404 ---three triangles meet at vertexes of tetrahedron, 91
405 ---four triangles meet at vertexes of octahedron, 91
406 ---five triangles meet at vertexes of icosahedron, 91
407 Volume The extent of space enclosed by geometric structures.
408 ---of tetrahedrons, 81
409 ---increased by tetrahedroning, 91
410 ---of octahedrons, 84
411 ---of cubes, 85
412413W
414 War
415 ---dangers of, 132-133, 135
416 Wave The pattern of motion produced by the transfer of energy through a medium. 48-49
417 Wavilinearity The property of all lines, which are always and inherently formed by wave motion.
418 ---nature operates through
419 Wilson, Woodrow, 14
420 Window The faces (areas or openings) of a system. 61
421 (continued from front flap)
422 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.
423 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.
424 Richard 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.
425 Jacket photo by Richard J. Brenneman
426 Jacket by Manuela Paul
427 St. Martin’s Press 175 Fifth Avenue New York, N.Y. 10010
428 PRINTED IN THE U.S.A.