About the author
2Amy C. Edmondson is Novartis Professor of Leadership and Management, Chair of Doctoral Programs at Harvard Business School, and Chair of the Committee of Higher Degrees in Business Studies at Harvard University. She is the Faculty Chair of the HBS World Bank Group program for new leaders. Edmondson has published over 50 articles in academic journals, management periodicals, and books.
3 Professor Edmondson teaches MBA and Executive Education courses in leadership, service management, and organizational learning, and a doctoral course in field research methods. She received her PhD in organizational behavior, AM in psychology, and AB in engineering and design, all from Harvard University.
4 In the late 1980s, Edmondson was Director of Research at Pecos River Learning Centers, where she worked closely with founder and CEO Larry Wilson to design and implement organizational change programs in a variety of Fortune 100 companies.
5 In the early 1980s, she worked as Chief Engineer for architect/inventor Buckminster Fuller, and her book, A Fuller Explanation, clarifies Fuller's mathematical contributions for a non-technical audience.
6 She lives with her husband George Daley, a physician-scientist, and their two young sons.
7 1 As mentioned in the "Note to Readers", quotations from Synergetics are followed by a numerical section reference, e.g. (216.03). References to Synergetics 2 append the letter "b" to the section number.
8 2These statements were included in many of Fuller's lectures. I am quoting from memory and from personal notes made over the years. Hereafter, assume this to be the source unless otherwise referenced.
9 3 See later chapters, especially Chapter 3 "Systems and Synergy for explanation of alloys, and Chapter 16 "Design Science" for discussion of Malthus.
10 4 See Spaceship Earth in Glossary.
(Glossarized terms are indicated by dotted underline.)
11 5 Sir Arthur Eddington, (1882–1944), English astronomer and physicist.
12 6 Quoted from epic 43-hour videotaped lecture session, Everything I Know, recorded over 10 days in January 1975. See Bibliography and Other resources (p.309) for details. Hereinafter cited as EIK video.
13 7 See e.g. Powers of Ten, by Philip and Phyllis Morrison and The Office of Charles and Ray Eames (New York: Freeman, Scientific American Books, 1982).
14 8 See Other resources (p.309) for biographical references.
15 9 Arthur L. Loeb, Space Structures (Reading, MA: Addison-Wesley, Advanced Book Program, 1976), p. xvii.
16 10F = GMm/r²: The attractive force due to gravity between two objects is equal to the "gravitational constant" (G) times the product of their masses and divided by the separation-distance raised to the second power.
17 11See Loeb's preface to Fuller's Synergetics: (p. xv) "In rejecting the predigested, Buckminster Fuller has had to discover the world by himself".
18 12Buckminster Fuller, Intuition (Garden City, N.Y.: Anchor Press/ Doubleday, 1973), p.39.
19 13Hugh Kenner, Bucky: A Guided Tour of Buckminster Fuller (New York: William Morrow,
1973), p.113.
See Glossary for definition of "Dymaxion".
20 14"Contribution to Synergetics" is a 52-page supplement by Arthur Loeb included in Fuller's Synergetics, pp. 821–876.
21 15Loeb, Space Structures, Chapter 6.
22 16Loeb, Space Structures, p.11.
23 17Chapter 5, Structure and "Pattern integrity", explains why "structural system" implies triangulated system.
24 18Loeb, Space Structures, p.40.
25 19Loeb, Space Structures, p.63.
26 20The derivation of the equation 3V E = 6, which is thought to have originated with Maxwell, can be derived from degree-of-freedom analysis of molecular spectra, and was applied by Loeb to polyhedral systems.
27 21Kenner, Bucky: A Guided Tour, pp.129–131.
28 22American Heritage Dictionary, 1970, "equilibrium".
29 23Amy Edmondson, "The Minimal Tensegrity Wheel" (thesis for completion of B.A. degree requirements, Harvard University, 1980), VES Teaching Collection, Carpenter Center, Harvard University.
30 24N. J. A. Sloane, "The Packing of Spheres", Scientific American (January 1984), p.116.
31 25Sloane, "The Packing of Spheres", p.116.
32 26I. Rayment, T. S. Baker, D. L. D. Caspar, and W. T. Murakami, "Polyoma Virus Structure at 22.5 Å Resolution", Nature, 295 (14 January 1982), p.110–115.
33 27Donald Caspar and Aaron Klug, "Physical Principles in the Construction of Regular Viruses", Cold Spring Harbor Symposia on Quantitative Biology, XXVII (1963), pp.1–3.
34 28See Glossary, "supplementary angles".
35 29A. L. Loeb, "Contribution to Synergetics", in Synergetics: The Geometry of Thinking (New York: Macmillan, 1975), pp. 860–875; "A Systematic Survey of Cubic Crystal Structure", Journal of Solid State Chemistry, 1 (1970), pp. 237–267.
36 30Refer to Chapter 5 Structure and "Pattern integrity" and Appendix C: Special Properties of the Tetrahedron.
37 31Loeb, "Contribution to Synergetics", pp.821–876.
Volume ratios are derived by comparing geometrically similar polyhedra so that "shape
constants" cancel out of the formulae. Credit for this approach belongs to Loeb and Pearsall, and
it must be noted that this section (H) of "Contribution to Synergetics" is adapted from an article
by Loeb in The Mathematics Teacher.
38 32Loeb, "Contribution to Synergetics", p.836.
39 33Loeb, "Contribution to Synergetics", p.832.
40 34Loeb, "Contribution to Synergetics", p.829.
41 35A. L. Loeb, "Addendum to Contribution to Synergetics", published in Synergetics 2: Further Explorations in the Geometry of Thinking, (New York: Macmillan Publishing, 1979), pp.473–476.
42 36Dennis Dreher of Bethel, Maine designed an onmidirectional hinging joint, which allows the necessary twisting of adjacent VE triangles in the jitterbug. This joint can be seen in Photo 11-1.
43 37Encyclopaedia Britannica, 1971, "Bohr, Niels".
44 38lsaac Asimov, Asimov's Guide to Science (New York: Basic Books, 1972), pp.334–335.
45 39Loeb, "Contribution to Synergetics", pp.836–847.
46 40Loeb, Space Structures, "Coda", pp.147–162.
47 41Loeb, "Contribution to Synergetics", pp.836–847.
48 42Discovered independently by Loeb and called "moduledra".
49 43Loeb, "Contribution to Synergetics" pp.847–855.
50 44Loeb, Space Structures, "Coda", pp.147–162.
51 45See Glossary and Chapter 15, "frequency of modular subdivision".
52 46Buckminster Fuller, Critical Path (New York: St. Martins Press, 1981), p.13.
53 47Recalling the principle of angular topology in Chapter 6 Angular Topology, we also know that the "angular takeout" is 720°. That is, if we subtract the sum of the surface angles at each vertex of a convex polyhedron from 360°, the sum of all these differences will be exactly 720°.
54 48Ernst Haeckel, Art Forms in Nature (New York: Dover, 1974), plate 1 (Radiolaria) and plate 5 (calcareous sponges).
55 49Buckminster Fuller, "Tensegrity", Creative Science and Technology, IV, No.3 (January–February, 1981), p.11.
56 50Letter from Ingber to Buckminster Fuller, April 5, 1983.
57 51This approach characterizes Fuller's "World Game" studies. See Other resources (p.309) for sources of information about this research.
58 52Buckminster Fuller and Shoji Sadao, Cartographers; © R. Buckminster Fuller, 1954. The word DymaxionTM and the DymaxionTM Map design are trademarks of the Buckminster Fuller Institute. © Buckminster Fuller Institute, 1938, 1967, 1992.
59 53Fuller, Critical Path, p. xxiii.