Introduction
1. Thomas Hobbes, Leviathan, ed. A. R. Waller (Cambridge: Cambridge University Press, 1908; 1935), p. 11. Parts of this Introduction appeared separately as “The Dimensions of Signs, Tools and Models,” Semiotica, 28 1/2 (1979): 63-82.
2. See his Human Nature: On the Fundamental Elements of Policy; Chapter 4; collected in Body, Man and Citizen: Thomas Hobbes, ed. Richard S. Peters (New York: Collier Books, 1967), p. 195. Conjecture is modern in the sense that it emerged with probability theory in the eighteenth century. See Ian Hacking, The Emergence of Probability (Cambridge: Cambridge University Press, 1975).
3. Elie Halevy, The Growth of Philosophic Radicalism (Boston: Beacon Press, 1955), p. 92.
4. For a brief history of the topic “symbolic space” see Ernst Cassirer, An Essay on Man (New Haven: Yale University Press, 1944), pp. 43-55. More recently in various essays now collected in Objective Knowledge (New York: Oxford University Press, 1974), Karl R. Popper has theorized about a category that he calls World III, which includes all of the intellectual records of human kind. For its application to physiology see John C. Eccles, Facing Reality: Philosophical Adventures by a Brain Scientist (New York: Springer-Verlag, 1970), pp. 164-73. Most pertinent to this introduction is Gerald Holton’s “proposition space,” which locates in a hypothetical dimension those thematic presuppositions of science that prompt both objective observation and analytic reason. See Thematic Origins of Scientific Thought: Kepler to Einstein (Cambridge, Mass.: Harvard Univeristy Press, 1973); and “On the Role of Themata in Scientific Thought,” Science 188 (25 April 1975): 328-38. See also Thomas A. Sebeok, “Problems in the Classification of Signs,” Studies for Einar Haugen, ed. Evelyn Scherabon Furchow et al. (The Hague: Mouton, 1972), p. 516.
5. Paul Watzlawick et al., Change: Principles of Problem Formation and Problem Resolution (New York: W. W. Norton & Co., 1974), pp. 9-10.
6. Julian S. Huxley, “The Courtship-habits of the Great Crested Grebe (Podicepts cristatus) ’, with an addition to the Theory of Sexual Selection,” Proceedings of the. . . Zoological Society of London 35 (1914): 491-562. For current work in zoosemiotics, see Animal Communication: Techniques of Study and Results of Research, ed. Thomas A. Sebeok (Bloomington: Indiana University Press, 1968). An important reexamination of palingenesis is found in Stephen Jay Gould’s Ontogeny and Phylogeny (Cambridge, Mass: Harvard University Press, 1977).
7. Edward O. Wilson, “Animal Communication,” Scientific American (September 1972), now collected in Communication: A Scientific American Book (San Francisco: W. H. Freeman Co., 1972), p. 35.
8. Konrad Lorenz, On Aggression, trans. Marjorie Kerr Wilson (New York: Bantam Matrix Edition, 1966), pp. 57-84. See also Thomas A. Sebeok, “Prefigurements of Art,” Semiotica, 281/1(1979).
9. Claude Lévi-Strauss, Tristes Tropiques: An Anthropological Study of Primitive Societies in Brazil, trans. John and Doreen Weightman (London: Atheneum, 1973), Chapter 25, “A Writing Lesson.”
10. G. Lukács, History and Class Consciousness: Studies in Marxist Dialectics (Cambridge, Mass.: M.I.T. Press, 1971), pp. 83-222.
11. Roman Jakobson, “Quest for the Essence of Language,” Diogenes 51 (Fall 1965):36. The entire issue is useful.
12. C. S. Peirce, “The Essence of Mathematics,” in Collected Papers of Charles Sanders Peirce, ed. Charles Hartshoren and Paul Weiss (Cambridge, Mass.: Harvard University Press, 1933), vol. 4.
13. Alfred North Whitehead, Science and the Modern World (New York: Macmillan Free Press, 1925; 1953), p. 21.
14. Translated by C. K. Ogden and I. A. Richards, The Meaning of Meaning: A Study of the Influence of Language upon Thought and of the Influence of the Science of Symbolism (New York: Harcourt, Brace and World, Inc., 1923), p. 5. See Ferdinande de Saussure, Course in General Linguistics, trans. Wade Baskin (New York: McGraw-Hill Co., 1966).
15. Rudolf Arnheim, Visual Thinking (Berkeley: University of California Press, 1969), especially the chapter “Words in Their Place.” In ordinary speech also, redundancy is insured by the use of different but parallel codes of discourse such as gesture and inflection. See Gregory Bateson, “Redundancy and Coding,” in Animal Communication, ed. Thomas A. Sebeok (Bloomington: Indiana University Press, 1968), pp. 614-26. This reinforcement of the message by different codes is called the “ribbon concept” or “multichannel communication” in Sebeok, “Problems in the Classification of Signs,” p. 517.
16. Jean Piaget, The Child’s Conception of Space, trans. F.J. Langdon and J. L. Lunzer (New York: W. W. Norton & Co., 1968), p. 17.
17. Arnheim, p. 180.
18. Johan Huizinga, Homo Ludens: A Study of the Play Element in Culture (Boston: Beacon Press, 1955).
19. E. A. Armstrong, “The Crane Dance in East and West,” Antiquity 17 (1943):71. For an overview see Joseph Needham, Science and Civilization in China (Cambridge: Cambridge University Press, 1954), 1:163.
20. See Robert Graves, The Greek Myths (New York: Penguin Books Inc., 1955) 1:316-17, for the linkage of hobbling in partridge-dance rituals with Hephaestus (Vulcan) and Tantalus. For Oedipus as Swollen Foot, “walking obliquely,” see Lévi-Strauss, “The Structural Study of Myth,” trans. Claire Jacobson and Brooke Grundfest Schoepf, in Structural Anthropology (New York: Anchor Books, 1963), pp. 214-15.
21. For George Derwent Thomson, Studies in Ancient Greek Society: The Prehistoric Aegean (New York: Citadel Press, 1965), 1:121, this clan emblem is but one of many “totemic survivals.”
22. For a discussion and a bibliography, see William G. Madsen, “Earth the Shadow of Heaven: Typological Symbolism in Paradise Lost, “in Milton: Modern Essays in Criticism, ed. Arthur E. Barker (New York: Oxford University Press, 1965), pp. 246-63.
23. José Ortega y Gasset, The Dehumanization of Art and Other Essays on Art, Culture and Literature (Princeton: Princeton University Press, 1968), p. 33.
24. Sigmund Freud, Civilization and Its Discontents, trans. James Strachey (New York: W. W. Norton & Co., 1962), p. 39.
25. Claude Lévi-Strauss, The Savage Mind, trans. George Weidenfield and Nicolson Ltd. (Chicago: The University of Chicago Press, 1966), pp. 16-19.
26. Joseph Needham, Science and Civilization in China (Cambridge: Cambridge University Press, 1971), 4:7, pp. 418-20.
27. For a discussion of the relics and their interpretation as the “cult of the ship,” see Max Raphael, Prehistoric Pottery and Civilization in Egypt, trans. Norbert Guterman (New York: Bollingen Foundation, 1947), pp. 136-37, 141-43.
28. José Ortega y Gasset, An Interpretation of Universal History, trans. Mildred Adams. (New York: W. W. Norton & Co., 1973), p. 73. For a semiotic interplay between economics and esthetics via the opportunity of ships, see my “Aesthetics of British Mercantilism,” New Literary History 11 (Winter 1980):303-21.
29. For a discussion see Karl R. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge (New York: Harper Torchbooks, 1962), p. 138..
30. George Thomson, Studies in Greek Philosophy: The Greek Philosophers, (New York: Citadel Press, 1965) 2:159.
31. See Raymond Williams, Culture and Society 1780-1950 (New York: Harper Torchbooks, 1958), p. 219.
32. For a critique of instrumentalism see Popper, Conjectures and Refutations, Chapter 3.
33. John Dewey, Art as Experience (New York: Capricorn Books, 1958), “The Act of Expression,” p. 64.
34. Charles Morris, Foundations of the Theory of Signs (Chicago: The University of Chicago Press, 1938). For a discussion see Umberto Eco, A Theory of Semiotics (Bloomington: Indiana University Press, 1976), p. 16.
35. Herman Von Helmholtz, Popular Scientific Lectures, trans. H. W. Eve (New York: Dover Publications, 1962), p. 5.
36. Plutarch, The Lives of the Noble Grecians and Romans, trans. John Dry-den (New York: Modern Library, 1932), p. 186.
37. Arturo Rosenbluth and Norbert Wiener, “The Role of Models in Science,’’ Philosophy of Science 12 (1945):316.
38. Herbert A. Snow, “The Architecture of Complexity,” Proceedings of the American Philosophical Society 106 (December 1962):479.
39. Ogden & Richards, p. 11.
40. Eco, pp. 56-57.
41. Martin Gardner, The Ambidextrous Universe: Left, Right, and the Fall of Parity (New York: Mentor Books, 1969), p. 153.
42. Erwin Panofsky, Galileo as a Critic of the Arts (The Hague: Martinus Nijhof, 1954), pp. 9-10.
43. J. Z. Young, An Introduction to the Study of Man (Oxford: Oxford University Press, 1971), p. 46.
Chapter 1
1. J. Bronowski, The Ascent of Man (Boston: Little, Brown & Co., 1973), p. 24. I am indebted to his chapter, “The Grain in the Stone,” for the important distinction between the hand’s analytic as averse to its moulding capacities.
2. Michael Polanyi, “Knowing and Being,” collected in Knowing and Being: Essays by Michael Polanyi, ed. Marjorie Grene (Chicago: University of Chicago Press, 1969), p. 125.
3. Sigfried Giedion, The Eternal Present: The Beginnings of Art (New York: Bollingen Foundation, 1962), pp. 93-100.
4. Max Raphael, Prehistoric Cave Paintings, trans. Norbert Guterman (New York: Bollingen Foundation, 1945), pp. 20-37.
5. J. Z. Young, An Introduction to the Study of Man (New York: Oxford University Press, 1971), p. 486.
6. Martin Gardner, The Ambidextrous Universe (New York: Mentor, 1969), Chapters 4, 22.
7. Joseph Needham, Science and Civilization in China (Cambridge: Cambridge University Press, 1954-), 2:45-46.
8. Cited by Alfred North Whitehead, Religion in the Making (New York: Macmillan Co., 1926), p. 74.
9. Rousseau, Emile, trans. Barbara Foxley (New York: E. P. Dutton, 1961), p. 151.
10. Giedion, p. 79.
11. Young, pp. 486-87.
12. Stuart Mosher, The Story of Money, Bulletin of the Buffalo Society of Natural Sciences, vol. 27, no. 2 (1936), p. 21.
13. Niels Bohr, Atomic Theory and the Description of Nature (Cambridge: Cambridge Univeristy Press, 1934), p. 99. For an overview of Bohr see Gerald Holton, “The Roots of Complementarity,” in Thematic Origins of Scientific Thought: Kepler to Einstein (Cambridge, Mass.: Harvard University Press, 1973), pp. 115-61. See also Holton’s “Conveying Science by Visual Presentation,” in Education of Vision, ed. Gyorgy Kepes (New York: G. Braziller, 1965), pp. 50-77, for an argument favoring the unsanitized reality of actual laboratory demonstration.
14. Polanyi, p. 127.
15. For a discussion of the pointing hand see Umberto Eco, A Theory of Semiotics (Bloomington: Indiana University Press, 1976), pp. 115-21. See also K. T. Fann, Wittgenstein’s Conception of Philosophy (Berkeley: University of California Press, 1969), p. 74.
16. See Ernst Cassirer, An Essay on Man (New Haven: Yale University Press, 1944), p. 206.
17. Martin Heidegger, An Introduction to Metaphysics, trans. Ralph Manheim (New Haven: Yale University Press, 1959), p. 1-3.
18. See Roman Jakobson, “A Few Remarks on Peirce, Pathfinder in the Science of Language,” Modern Language Notes 92 (December 1977): 1029-030, for invariance.
19. Emmon Bach, “Structural Linguistics and the Philosophy of Science,” Diogenes 51 (Fall 1965): 111-28.
20. Raphael, p. 57.
21. See Giedion’s Conclusion, “The Space Conception of Prehistory,” 1:513-38.
22. See Peter Tompkins, Secrets of the Great Pyramid (New York: Harper and Row, 1971), p. 46. For an introduction to pyramidal mathematics, see Lancelot Hogben, Science for the Citizen (London: George Allen & Unwin Ltd., 1940), Chapter 1, “Pole Star and Pyramid.”
23. Arthur H. Robinson and Barbara Bartz Petchenik, The Nature of Maps (Chicago: The University of Chicago Press, 1976), p. 14.
24. Claude Lévi-Strauss, “Split Representation in the Art of Asia and America,” in Structural Anthropology, trans. Claire Jacobson and Brooke Grundfest Schoepf (Garden City: Anchor Books, 1967), pp. 260-61.
25. Thomas Hobbes, Leviathan, ed. A. R. Waller (Cambridge: Cambridge University Press, 1935), p. 9.
26. Young, pp. 516, 46-50.
27. For a discussion see Gerald M. Weinberg, An Introduction to General Systems Thinking (New York: John Wiley and Sons, 1975), pp. 87-94.
28. Jean Piaget, Genetic Epistemology, trans. Eleanor Duckworth (New York: W. W. Norton & Co., 1970), p. 43. For a good textbook based on Piaget’s topological theory, see David J. Fuys and Rosamund Welchman Tischler, Teaching Mathematics in the Elementary School (Boston: Little, Brown & Co., 1979).
29. James D. Watson, The Double Helix: A Personal Account of the Discovery of the Structure of DNA (New York: Signet, 1969), p. 136.
30. Thomas A. Sebeok, “Goals and Limitations of the Study of Animal Communication,” in Animal Communication, ed. Thomas A. Sebeok (Bloomington: Indiana University Press, 1968), p. 12. For a discussion of the role of genetic information within the general system of cellular communication, see Gunther S. Stent, “Cellular Communication,” in Communication, (San Francisco: W. H. Freeman & Co., 1972), pp. 17-25.
31. Young, p. 47.
32. See Gardner, Chapters 12, 13, 14 for a discussion of the handedness of carbon molecules, the conventions of describing two-dimensional and three-dimensional chemical models, and the structure of DNA.
33. John Dewey, Art as Experience (New York: Putnam Capricorn, 1958), Chapter 8, “The Organization of Energies.” See also James Bunn, “Circle and Sequence in the Conjectural Lyric,” New Literary History 3 (1971-1972):511-26, for a discussion of Dewey’s ideas about rhythm.
34. Henri Bergson, Creative Evolution, trans. Arthur Mitchell (New York: Modern Library, 1944), p. 328.
35. Jean Piaget and Barbara Inhelder, The Child’s Conception of Space, trans. F.J. Langdon and J. L. Lunzer (New York: W. W. Norton & Co., 1967), Chapter 4, “The Study of Knots and the Relationship of ‘Surrounding.’ “For a recent discussion of topology and knotting, see Lee Neuwirth, “The Theory of Knots,” Scientific American, vol. 240, June 1979, pp. 110-24.
36. See Jane S. Richardson, “B-Sheet Topology and the Relatedness of Proteins,” Nature, vol. 268, 11 August 1977, pp. 495-500.
37. Johann Wolfgang von Goethe, Italian Journey 1786-1788, trans. W. H. Auden and Elizabeth Mayer (New York: Schocken, 1968), pp. 401-02.
38. See A. H. Church, The Relation of Phyllotaxis to Mechanical Law (London: Williams and Norgate, 1904), p. 1. Cited by H. S. M. Coxeter, Introduction to Geometry, 2d ed. (New York: John Wiley & Sons, Inc., 1969), p. 169.
Chapter 2
1. Bertram D. Lewin, The Image and the Past (New York: International Universities Press, 1968), pp. 33-41.
2. Rudolph E. Heyman, “An Approach to Early Art through Technical Drawing,” Proceedings of the Tenth International Congress of the History of Science (Paris: 1964), pp. 373-75.
3. Frances Yates, The Art of Memory (Chicago: The University of Chicago Press, 1966).
4. Rudolph Arnheim, Visual Thinking (Berkeley: University of California Press, 1969), p. 137.
5. P. W. Bridgman, The Way Things Are (Cambridge, Mass.: Harvard University Press, 1959), p. 34.
6. Karl R. Popper, “Back to the Presocratics,” in Conjectures and Refutations, (New York: Harper Torchbooks, 1965), pp. 136-65.
7. I. J. Gelb, A Study of Writing (Chicago: The University of Chicago Press, 1963), p. 12.
8. Denise Schmandt-Besserat, “An Archaic Recording System and the Origin of Writing,” Syro-Mesopotamian Studies 1 (July 1977):31-70.
9. Charles H. Kahn, Anaximander and the Origin of Greek Cosmology (New York: Columbia University Press, 1960), p. 82.
10. Popper, p. 139.
11. Lancelot Hogben, Science for the Citizen (London: George Allen & Unwin Ltd., 1938; 1966), p. 105. Also Joseph Needham, Science and Civilization in China (Cambridge: Cambridge University Press, 1954-), 1:231 for a simultaneous appearance in China.
12. Hogben, p. 74.
13. J. Z. Young, An Introduction to the Study of Man (New York: Oxford University Press, 1971), p. 497.
14. Cited by Arnheim, “Models for Theory,” a chapter from which many of my conjectures derive.
15. Cited by Alexander Koyré, From the Closed World to the Infinite Universe (Baltimore: The Johns Hopkins University Press, 1957), p. 117.
16. See Walter J. Ong, “System, Space and Intellect in Renaissance Symbolism,” collected in The Barbarian Within and Other Fugitive Essays (New York: Macmillan, 1962).
17. For a discussion, see Erwin Panofsky, Albrecht Dürer (Princeton: Princeton University Press, 1945). The Chapter “Dürer as a Mathematician,” is in James R. Newman’s four-volume anthology The World of Mathematics (New York: Simon & Schuster, 1956), 1:603-21. See also Ernst H. Gombrich, Art and Illusion: A Psychology of Pictorial Representation (Princeton: Bollingen Foundation, 1961), p. 306.
18. See Morris Kline, Mathematical Thought from Ancient to Modern Times (New York: Oxford University Press, 1972), pp. 308-19, and Lancelot Hogben, Mathematics for the Millions (New York: W. W. Norton & Co., 1964), p. 346.
19. For Mario Praz, this is a typical Mannerist painting. See Mnemosyne: The Parallel between Literature and the Visual Arts (Princeton: Bollingen Foundation, 1967), p. 93.
20. Marshall McLuhan and Harley Parker, Through the Vanishing Point: Space in Poetry and Painting (New York: Harper Colophon Books, 1968), p. 55.
21. Kline, p. 302.
22. See Kline, pp. 320-21, for three-dimensional coordinate geometry. See Gerald Holton, Thematic Origins of Scientific Thought: Kepler to Einstein (Cambridge: Harvard University Press, 1973), pp. 25-26, 53-60, for a model of scientific analysis that uses three-dimensional coordinates.
23. See Panofsky, p. 675.
24. Richard Courant and Herbert Robbins, “Euler’s Formula for Polyhedra,” What is Mathematics? (Oxford: Oxford University Press, 1941), in Newman, 1:581.
25. Franz Boas, Primitive Art (New York: Dover Publications, 1955), p. 223. See also Claude Lévi-Strauss, “Split Representation in the Art of Asia and America,” in Structural Anthropology, trans. Claire Jacobson and Brooke Grundfest Schoepf (New York: Anchor, 1967), pp. 245-68.
26. See Erwin Panofsky, Galileo as a Critic of the Arts (The Hague: Martinus Nijhof, 1954), pp. 13-16.
27. D’Arcy Wentworth Thompson, On Growth and Form, ed. J. T. Bonner, abridged ed. (Cambridge: Cambridge University Press, 1961). See also Stephen Jay Gould, “D’Arcy Thompson and the Science of Form,” New Literary History 2 (Winter 1971).
28. Ludwig Wittgenstein, Tractatus Logico-Philosophicus (London: Routledge & Kegan Paul, 1922), p. 177.
29. Bertrand Russell, The ABC of Relativity, ed. Felix Pirani, 3d rev. ed. (London: Signet, 1969), pp. 79-81.
30. A related phenomenon in contemporary diagrammatics is René Thorn’s catastrophe theory. See E. C. Zeeman, “Catastrophe Theory,” Scientific American 234 (April 1976):65-83.
31. For a useful compilation of Peirce’s disparate writings about the trichotomy of signs into icon, index, and symbol, see Philosophical Writings of Peirce (New York: Dover Publications, 1955), pp. 98-119.
32. James J. Gilson, The Perception of the Visual World (Boston: Houghton Mifflin, 1950). His distinction has been useful to Rudolph Arnheim, Art and Visual Perception: A Psychology of the Creative Eye, rev. ed. (Berkeley: University of California Press, 1974), to Gombrich, and to Wylie Sypher, Literature and Technology: The Alien Vision (New York: Vintage Books, 1968). See especially Don Ihde, Experimental Phenomenology: An Introduction (New York: Capricorn Books, 1977), Chapter 3.
33. See E. H. Gombrich, “The Visual Image” in Communication (San Francisco: W. H. Freeman, 1972), pp. 46-62.
34. Arnheim, Visual Thinking, p. 231.
35. For a different perspective on binary thinking, see Philip Morrison, “The Modularity of Knowing,” in Module, Proportion, Symmetry, Rhythm, ed. Gyorgy Kepes (New York: G. Braziller, 1966). pp. 1-19.
36. See F. Vaihinger, The Philosophy of “As If”: A System of the Practical and Religious Features of Mankind, trans. C. K. Ogden (New York: Harcourt, Brace & Co., 1924), pp. 179-82.
Chapter 3
1. See Theodore Mommsen, Corpus Inscriptionuua Latinarum (Berlin: Apud Weidmannos, 1918), vol. 1, parts 1 and 2.
2. Most of my discussion of time’s arrow is drawn from C.J. Whitrow, The Natural Philosophy of Time (London: Thomas Nelson, 1961), and his Nature of Time (Baltimore: Penguin Books, 1975).
3. Whitrow, Nature of Time, pp. 123, 135.
4. Ibid., p. 135.
5. Whitrow, Natural Philosophy of Time, pp. 74-75.
6. Ibid., pp. 228, 293.
7. Cited by Roman Jakobson, “Quest for the Essence of Language,” Diogenes 51 (Fall 1965): 36-37. From Peirce’s Existential Graphs, 4:360.
8. Whitrow, Natural Philosophy of Time, pp. 295-96.
9. Michael Polanyi, Personal Knowledge: Towards a Post-Critical Philosophy (Harper Torchbooks, 1964), pp. 393-402.
10. Umberto Eco, A Theory of Semiotics (Bloomington: Indiana University Press, 1976), pp. 68-72.
11. Whitrow, Nature of Time, p. 29.
12. Bertrand dejouvenal, The Art of Conjecture, trans. Nikita Lary (New York: Basic Books, 1967), p. 27.
13. For example, see “An American Indian Model of the Universe,” collected in Language, Thought and Reality: Selected Writings of Benjamin Lee Whorf ed. John B. Carroll (Cambridge, Mass.: The M.I.T. Press, 1956). For an overview of tense and time in different languages, see John B. Lyons, Introduction to Theoretical Linguistics (Cambridge, Mass.: Cambridge University Press, 1968), pp. 304-06.
14. Alfred North Whitehead, Science and the Modern World (New York: Macmillan, 1925; 1953), p. 24.
15. Karl Menninger, Number Words and Number Symbols: A Cultural History of Numbers, trans. Paul Broneer (Cambridge, Mass.: The M.I.T. Press, 1969). For his discussion of tally sticks, to which this section is indebted, see pp. 223-51.
16. Alexander Marshack, The Roots of Civilization: The Cognitive Beginnings of Man’s First Art, Symbol and Notation (New York: McGraw-Hill, 1972).
17. Morris Kline, Mathematical Thought from Ancient to Modern Times (New York: Oxford University Press, 1972), pp. 1199-201.
18. Whitehead, p. 27.
19. The Born-Einstein Letters: Correspondence between Albert Einstein and Max and Hedwig Born, From 1916-1945 (New York: Walker and Co., 1971), p. 95.
20. Lancelot Hogben, Mathematics for the Million (New York: W. W. Norton, 1968), p. 40.
21. For a discussion of Newton’s attitude toward these mysteries, see Frank Manuel, A Portrait of Newton (Cambridge, Mass.: Harvard University Press, 1968), pp. 391, 467. For an excellent analysis of Newton’s beliefs in this regard, springing from the tradition of Cambridge Platonism, see J. E. McQuire and P. M. Rattansi, “Newton and the ‘Pipes of Pan,’“ Notes and Records of the Royal Society of London 21 (1966): 108-43.
22. Bertrand Russell, The ABC of Relativity (New York: Signet, 1956), p. 63.
23. James R. Newman, The World of Mathematics (New York: Simon and Schuster, 1956), 1:80. See also Russell, p. 63, for the rule of thumb about 3-4-5 units of length. See also, Hogben, pp. 47-48. See also Joseph Needham, Science and Civilization in China (Cambridge: Cambridge University Press, 1954-), 4:167-213, for an extensive comparison of Pythagorean and Chinese harmonics.
24. For an overview, see Edward A. Lippman, Musical Thought in Ancient Greece (New York: Columbia University Press, 1964). Also Isabel Henderson, “Ancient Greek Music,” in New Oxford History of Music: Ancient and Oriental Music (London: Oxford University Press, 1957), 1:341ff.
25. Kline, p. 148.
26. Lippman, p. 136.
27. The sketch of nodes, fingers, and vibrating strings—but not the triangular conjecture—has been adopted from a vivid photograph in Jacob Bronowski’s The Ascent of Man (Boston: Little, Brown, 1973), p. 154.
28. For an introduction to the rationale of Pythagorean cosmology, see Milton C. Nahm, Selections from Early Greek Philosophy (New York: Apple-ton-Century-Crofts, 1934), pp. 5-52; and almost any scholarly edition of Plato’s Timaeus includes at least a brief discussion of the tetractys and Plato’s “soul stuff.”
29. Needham, pp. 178-80.
30. McGuire and Rattansi, p. 115.
31. P. W. Bridgman, Dimensional Analysis, rev. ed. (New Haven: Yale University Press, 1937), p. 154. Einstein often wrote about logical errors regarding time. See Gerald Holton, “Constructing a Theory: Einstein’s Model,” American Scholar (Summer, 1979), 309-40, but especially, 315-17.
32. Whitehead, pp. 49-51, 55, 58-59, 144-48. This ‘orthodox’ view was not unchallenged in the seventeenth and eighteenth centuries. See, for instance, Henry More’s argument with Descartes about the latter’s stipulation that mind exists, but not in space, summarized in Alexander Koyré, From the Closed World to the Infinite Universe (Baltimore: Johns Hopkins University Press, 1957), Chapter 5; also in Basil Willey, The Seventeenth-Century Background: The Thought of the Age in Relation to Religion and Poetry (New York: Doubleday Anchor, 1934), Chapter 8. Both are indebted to E. A. Burtt’s “Conclusion” to The Metaphysical Foundations of Modern Physical Science (New York: Doubleday Anchor, 1924; 1932). For a discussion of the pernicious mis-influence of the phrase “in the mind,” see Isaiah Berlin, The Age of Enlightenment (New York: Mentor Books, 1956), “Introduction,” and commentary upon David Hume. Karl R. Popper calls this kind of container a “bucket” theory of mentation, in The Open Society and its Enemies, 3d ed. (Princeton: Princeton University Press, 1957), 2:213-.
33. Whitrow, Natural Philosophy, p. 113.
Chapter 4
1. See Gunther S. Stent, “Cellular Communication,” in Communication (San Francisco: W. H. Freeman, 1972), pp. 17-25.
2. Morton Bloomfield, “The Study of Language,” Daedalus 102, no. 9 (Summer 1973), p. 9.
3. Ferdinand de Saussure, Course in General Linguistics, ed. Charles Bally et al., trans. Wade Baskin (New York: McGraw-Hill, 1966), Chapter 3. For an authoritative overview of twentieth-century linguistics, with Saussure at its center, see Roman Jakobson, Main Trends in the Science of Language (New York: Harper Torchbooks, 1973), Chapter 1, “Linguistic Vistas.”
4. G.J. Whitrow, The Natural Philosophy of Time (London: Thomas Nelson, 1961), p. 153. Furthermore, a historical sketch of the idea of space-time, indeed, the very notion of four-dimensional thinking, would be inadequate without reference to Hermann Minkowski. See Peter Louis Galison’s essay about discovery, “Minkowski’s Space-Time: From Visual Thinking to the Absolute World,” in Historical Studies in the Physical Sciences, eds. Russell McCormach, Lewis Pyenson, and Roy Steven Turner (Baltimore: Johns Hopkins University Press, 1979), pp. 85-121.
5. Roman Jakobson, “Verbal Communication,” in Communication, pp. 39-42.
6. Jakobson cites Gerald Holton’s work about Einstein. See his Thematic Origins of Modern Science (Cambridge, Mass.: Harvard University Press, 1973), Chapters 5-10.
7. Jean Piaget, Structuralism, trans. Chaninah Maschler (New York: Basic Books, 1970), p. 54.
8. Kurt Koffka, Principles of Gestalt Psychology (New York: Harbinger Book, 1935), p. 41.
9. See C. H. Waddington, Behind Appearances, A Study of the Relations between Painting and the Natural Sciences in this Century (Cambridge, Mass.: M.I.T. Press, 1969).
10. Piaget, pp. 13-16.
11. Johannes von Uexküll, Theoretical Biology (New York: Harcourt, Brace & Co., 1926). Cited by Ernst Cassirer, An Essay on Man, (New Haven: Yale University Press, 1944), pp. 23-24.
12. Ludwig von Bertalanffy, General System Theory: Foundations, Developments, Applications (New York: George Braziller, 1968), pp. 10-17. But see also Piaget’s Structuralism, pp. 44-48. A good introduction is Weinberg’s An Introduction to General System Theory (New York: John Wiley & Sons, 1975). For the importance of Whitehead’s concept of “organization,” see Waddington, pp. 109-15.
13. Francois Jacob, The Logic of Life: A History of Heredity, trans. Betty E. Spillman (New York: Pantheon, 1973), p. 190. All of Chapter 2, on “Organization,” is valuable for its historical overview.
14. Perhaps the most thorough recent survey of Romantic thought is M. H. Abrams, Natural Supernaturalism: Tradition and Revolt in Romantic Literature (New York: W. W. Norton & Co., 1971). For a discussion of a Romantic philosophy based on the metaphor of the flower, see Abrams, pp. 431-62.
15. Goethe, Italian Journey 1786-1788, trans. W. H. Auden and Elizabeth Mayer (New York: Schocken, 1968), pp. 251-52.
16. Stephen Jay Gould, “Evolutionary Paleontology and the Science of Form,” Earth-Science Reviews 6 (1970):97.
17. This discussion of Schlegel is taken from Thomas A. Sebeok, “Goals and Limitations of the Study of Animal Communication,” in Animal Communication: Techniques of Study and Results of Research, ed. Thomas A. Sebeok (Bloomington: Indiana University Press, 1968), p. 4. See especially Noam Chomsky, Cartesian Linguistics: A Chapter in the History of Rationalist Thought (New York: Harper & Row, 1966), pp. 19-31 for an insightful study of Schlegel and Goethe as generative grammarians from an “Urform.” The new wave of variation-invariance in turn-of-the-century mathematics may have sprung from a commonplace of Romantic organicism.
18. Ann Harleman Stewart, Graphic Representation of Models in Linguistic Theory (Bloomington: Indiana University Press, 1976). Chapter 1 is called “Tree Models.”
19. Arthur Koestler, “Beyond Atomism and Holism—the Concept of the Holon,” in Beyond Reductionism: New Perspectives in the Life Sciences, ed. Arthur Koestler and A. R. Smythies (Boston: Hutchinson Publishing Group, 1969), p. 193.
20. D’Arcy Thompson, On Growth and Form, ed. John Tyler Bonner, abridged ed. (Cambridge University Press, 1969), p. 61.
21. Gyorgy Kepes, Arts of the Environment (New York: George Braziller, 1972), p. 3.
22. José Ortega y Gasset, An Interpretation of Universal History (New York: W. W. Norton Co., 1973), p. 35.
23. See Robert S. Brumbaugh, Ancient Greek Gadgets and Machines (New York: Thomas Y. Crowell Co., 1966), Chapter 4, “Scientists and Model Makers.”
24. Joseph Needham, Science and Civilization in China (Cambridge: Cambridge University Press, 1954-), 2:125.
25. Lynn White, Jr., “Technology and Invention in the Middle Ages,” Speculum 15 (April 1940): 153.
26. The following discussion is taken from H. W. Dickinson, James Watt, Craftsman and Engineer (Cambridge: Cambridge University Press, 1936).
27. Sebeok, p. 12.
28. For a running attack on reductionism, see Koestler and Smythies.
29. See Jacques Monod, Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology (New York: Alfred A. Knopf, 1971), pp. 79-80.
30. Jacob, pp. 7-8.
31. Thomas S. Kuhn, The Logic of Scientific Discovery, rev. ed. (Chicago: The University of Chicago Press, 1970), the section on “Normal Science.”
32. Piaget, p. 34.
33. John Dewey, Art as Experience (New York: Capricorn Books, 1958), p. 169.
Conclusion
1. John Locke, An Essay Concerning Human Understanding, ed. Peter H. Nidditch (Oxford: Oxford University Press, 1975), Book 2, p. 204. For a commentary about the modernism of the passage, see G.J. Whitrow, Natural Philosophy of Time (London: Thomas Nelson, 1961), p. 223.
2. E.J. Hobsbawm, The Age of Revolution 1789-1848 (New York: Mentor, 1962), pp. 45-46.
3. Frank E. Manuel, The Age of Reason (Ithaca: Cornell University Press, 1951), p. 74. See also Jacques Ellul, The Technological Society, trans. John Wilkinson (New York: Vintage, 1964), pp. 87-92, where technical innovations augment one another in a geometrical progression, i.e., “acceleration,” p. 421.
4. Henry Adams, The Education of Henry Adams (New York: Modern Library, 1931); The Degradation of the Democratic Dogma (New York: Mac-Millan, 1920); and Brooks Adams, The Law of Civilization and Decay: An Essay on History (1896; New York: Alfred Knopf, 1943).
5. See Henry Adams’ chapter “The Rule of Phase Applied to History,” Degradation, p. 308. Gerald Piel cites this passage in The Acceleration of History (New York: Alfred Knopf, 1972), p. 23. He diagrams a number of exponential curves that mirror an end of economic abandon in an era of accelerating complexity. For a similar meditation, beginning with Adams, see Gunther S. Stent, Paradoxes of Progress (San Francisco: W. H. Freeman & Co., 1978), Chapter 1, “The Ends of Progress.”
6. Manuel, p. 80.
7. Albert Einstein, “Morals and Emotions,” in Out of My Later Years (New York: Littlefield, Adams & Co., 1950), p. 21.
8. Ernst Cassirer, An Essay on Man (New Haven: Yale University Press, 1944), p. 25.
9. See Bertrand de Jouvenal, “Rousseau’s Theory of Government,” in Hobbes and Rousseau: A Collection of Critical Essays, ed. Maurice Cranston and Richard S. Peters (Garden City, N.Y.: Anchor, 1972), pp. 484-97. For a discussion of the metaphor of balance and mixed forms of government with respect to British historiography, see my “The Tory View of Geography,” Boundary 2, vol. 7, no. 2 (Winter 1979), pp. 149-67.
10. Rousseau, The Social Contract, Book 3, Chapter 1; cited by jouvenal, p. 492.
11. Rousseau, Letters from the Mountain; cited by jouvenal, p. 495.
12. See An Essay on the Principle of Population, ed. Philip Appleman (New York: Norton Critical Edition, 1976).
13. D’Arcy Wentworth Thomson, On Growth and Form, abridged ed., ed. John Tyler Bonner (Cambridge: Cambridge University Press, 1961), p. 35.
14. Henry Adams, Degradation, pp. 306-07.
15. Martin Heidegger, An Introduction to Metaphysics, trans. Ralph Manheim (Garden City, N.Y.: Anchor, 1961).
16. Hannah Arendt, The Human Condition (Chicago: The University of Chicago Press, 1958), p. 102.
17. Edward O. Wilson, On Human Nature (Cambridge, Mass: Harvard University Press, 1978), “Glossary.”
18. Paul Garvin, “Linguistics and Semiotics,” Semiotica 20 1/2(1977): 106.
19. Jouvenal, Art of Conjecture, pp. 93-95.
20. Stent, p. 52.
21. Morris Kline, Mathematical Thought from Ancient to Modern Times (New York: Oxford University Press, 1973), p. 33. See also Cassirer, p. 212.
22. Raymond Williams, Keywords: A Vocabulary of Culture and Society (New York: Oxford University Press, 1976), p. 29. See also “In Praise of Alienation,” Chapter 1 of Herbert N. Schneidau’s Sacred Discontent: The Bible and the Western Tradition (Baton Rouge: Louisiana State University Press, 1976).
23. Isaiah Berlin, Karl Marx: His Life and Environment (New York: Oxford University Press, 1939; 1963), pp. 137-38.
24. Arendt, pp. 102, 137.
25. “Reification” is the term used by Georg Lukacs in order to translate Marx’s phrase “commodity fetishism,” in History and Class Consciousness: Studies in Marxist Dialectics, trans. Rodney Livingston (Cambridge, Mass.: M.I.T. Press, 1971); see the chapter “Reification and the Consciousness of the Proletariat,” pp. 83-222. For a discussion, see Lucien Goldmann, Lukacs and Heidegger: Towards a New Philosophy, trans. William Q. Boel-hower (London: Routledge & Kegan Paul, 1977), pp. 27-29.
26. Wylie Sypher, Literature and Technology: The Alien Vision (New York: Vintage, 1968), pp. 196-97.
27. Selections from Early Greek Philosophy, trans. Milton C. Nahm (New York: Appleton-Century-Crofts, 1934; 1964), p. 281. For a discussion of suitability with respect to Greek thought, see Wladyslaw Tatarkiewicz, History of Aesthetics, vol. 1, Ancient Aesthetics, trans. Adam and Ann Czerniawski (The Hague: Mouton, 1970), pp. 95-102.
28. Einstein, p. 27.
29. For a discussion of the work of art removed from its originating context, see my “Aesthetics of British Mercantilism,” New Literary History 11 (Winter 1980).
30. Ralph Waldo Emerson, “Thoreau,” in Lectures and Biographical Sketches (Boston: Houghton, Mifflin & Co., 1904), 10:464.
31. Herman Melville, Moby-Dick, or, The Whale (New York: W. W. Norton & Co., 1967), “The Carpenter,” pp. 458-59.
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