Notes

1. . C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (Urbana: University of Illinois Press, 1949), p. 104.
2. . Ibid., 131). 100–101: The formal equation is H=−Σ pilog pi, where H the amount of information and Σ is the sum of the probabilities of each message expressed in logarithms to the base 2. E.g., if I have only two choices of content and send one, say by using lights in a church steeple, the total amount of information thus conveyed is the logarithm of 2 to the base 2, which equals 1 or unity (we recall that the logarithm of x to the base 2 will be the power to which 2 must be raised in order to equal x). John Tukey called this unit of information a “bit,” a term he created by condensing the longer term “binary digit,” which is related to the binary digit system (0 and 1). It may be recalled that the binary digit system not only is applicable to information theory but also nicely parallels the minimal capabilities of machine language where one can use the presence (+) or absence (0) of an electrical impulse to designate either of the two digits. By using bits as our units of information measurement we can see that “if one has available say 16 alternative messages among which he is equally free to choose, then since 16 = 24 so that log2 16 = 4, one says that this situation is characterized by 4 bits of information.”
3. . Ibid., p. 104.
4. . Example suggested by J. C. Robertson.
5. . Shannon and Weaver, p. 112.
6. . Roy Rappaport, “Ritual, Sanctity, and Cybernetics,” American Anthropologist 73 (1971): 59–76, and Pigs for the Ancestors: Ritua.1 in the Ecology of a New Guinea People (New Haven, Conn.: Yale University Press, 1968).
7. . Sigmund Freud, “Obsessive Actions and Religious Practices” (1907), in The Standard Edition of the Complete Psychological Works of Sigmund Freud, trans. and ed. James Strachey et al., 24 vols. (London: Hogarth Press, 1953–74), 9 (1959): 115–27.
8. . Herbert A. Simon, The Sciences of the Artificial (Cambridge, Mass.: M.I.T. Press, 1969).
9. . Ibid., p. 111.
10. . Herbert Spencer, Principles Of ‘Sociology, ed. S. Andreski (1896; London: Macmillan Co., 1969); Karl Marx, “The Communist Manifesto” (1848) in Capital: The Communist Manifesto and Other Writings by Karl Marx, ed. M. Eastman (New York: Modern Library, 1932), pp. 315–55; Talcott Parsons, Societies: Evolutionary and Comparative Perspectives, Foundations of Modern Sociology Series (Englewood Cliffs, N.J.: Prentice‐Hall, Inc., 1966).
11. . Jean Piaget, Structuralism, trans. and ed. Chaninah Maschler (New York: Basic Rooks, 1970); Harley C. Shands and James D. Meltzer, Language and Psychiatry (The Hague: Mouton, 1973); Noam Chomsky, Cartesian Linguistics: A Chapter in the History of Rationalist Thought (New York: Harper & Row, 1966).
12. . D'Arcy Thompson, On Growth and Form, 2d ed. (Cambridge: Cambridge University Press, 1942), pp. 1028–29; William Keith Chambers Guthrie, A History of Greek Philosophy, vol. 1 (The Early Presocratics and the Pythagoreans) (Cambridge: Cambridge University Press, 1962), pp. 181–319; F. M. Cornford, “Mysticism and Science in the Pythagorean Tradition,” Classical Quarterly 16(1922): 137–50 and 17 (1923): 1–12.
13. . W. Ross Ashby, An introduction to Cybernetics (London: Chapman & Hall, Ltd., 1956), p. 262.
14. . Simon, p. 110.
15. . Ibid; Walter Buckley, Sociology and Modern Systems Theory (Englewood Cliffs, N.J.: Prentice‐Hall, Inc., 1967).
16. . Simon; H.Jacobson, “Information, Reproduction, and the Origin of Life,” American Scientist  43 (1955): 119–27.
17. . Simon estimates that the watchmaker, named Hora, who uses subassembly in his procedures will make 111 times as many complete assemblies per watch as his competitor, Tempus. Assigning an arbitrary assembly time to each operation and a similar number of interruptions to, each, he figures that it will take Tempus four thousand times as long as Hora to complete a single watch (Simon, pp. 91–93).
18. . Ashby.
19. . Ashby compares the time required to find a single atom somewhere in the universe of 1073 atoms (1) by examining each atom at a time or (2) by asking of the entire set,“… is the atom in this half or that?” (ibid., p. 261). In the former it would take more centuries than this page has room to enumerate. In the latter, provided that one can ask the “this or that” question in a second, it would take only four minutes to find that single atom. The formula for the latter operation obviously is X = 1/2n, where X = the number of atoms remaining and n = the number of trials. Thus we can see the total number of atoms remaining to be examined after only twenty seconds of picking is equal to one‐half to the twentieth power or about one‐millionth of the original number.
20. . For examples of hierarchical analyses of religious and psychological systems see Parsons (11. 10 above); H. Mol, Identity and the Sacred (New York: Free Press, 1976); Gregory Bateson, Steps to an Ecology of Mind: Collected Essays in Anthropology, Psychiatry, Evolution, and Epistemology (San Francisco: Chandler Publishing Co., 1972); Anthony F. C. Wallace, Religion: An Anthropological View (New York: Random House, 1966); Eliot D. Chapple, Culture and Biological Man: Explorations in Behavioral Anthropology (New York: Holt, Rinehart & Winston, 1970); David Rapaport, “The Structure of Psychoanalytic Theory: A Systematizing Concept,” Psychological Issues 2, no. 2 (1960): 1–159; Karl H. Pribram and Merton M. Gill, Freud's “Project” Re‐Assessed (New York: Basic Books, 1976); Emanuel Peterfreund and Jacob T. Schwartz, “Information, Systems, and Psychoanalysis: An Evolutionary Biological Approach to Psychoanalytic Theory,” Psychological issues 7, nos. 1–2 (1971): 1–399; John E. Gedo and Arnold Goldberg, Models of the Mind (Chicago: University of Chicago Press, 1973). For reviews 01 applications of cybernetics to social sciences see Buckley (n. 15 above) and Roy R. Grinker, “The Relevance of General Systems Theory to Psychiatry,” in American Handbook of Psychiatry, ed. Silvano Arieti, 2d ed., 6 vols. (New York: Basic Books, 1974–75), 6 (1975): 251–72.21. Cf. Sigmund Freud, “Group Psychology and the Analysis of the Ego” (1921) in Strachey et al. (n. 7 above) 18 (1955): 67–143.
21. . A. W. H. Adkins, Merit and Responsibility: A Study in, Greek Values (Oxford: Oxford University Press, 1960), pp. 46–57.
22. . Religious institutions might well incorporate content redundancy in two distinct forms: content which represents or mirrors a generalized perception of the sacred and profane worlds and content which only indirectly models those worlds. The first type of content is similar to that which E. Jacobson (The Self and the Object World [New York: International Universities Press, 19641) analyzes in the conscious and unconscious fantasies of normal psychic life. The second would be similar to that which design theorists mean by the term “model”: “To an observer B, an object A* is a model of an object A* to the extent that B can use A* to answer questions that interest him about A” (M. I,. Minsky, as quoted by Margaret A. Boden in her Purposive Explanation in Psychology [Cambridge, Mass.: Harvard University Press, 1972], p. 125). Thus model and object need not be identical “forms” in order for the first to give one useful information about the nature of significant relationships among component parts of the second (Simon [n. 8 above], p. 17).
23. . Simon, p. 110.
24. . Although it is not easy to conceive of one. This may say something about the logic of the term “complexity” in normal discourse. While one can imagine a complex system, say the intertwining roads of an ancient, unplanned city that follows no structural/ formal laws of any sort, one would have difficulty imagining that he could find his way around it very easily.
25. . Ludwig Wittgenstein, Philosophical Investigations, trans. G. E. M. Anscombe, 3d ed. (New York: Macmillan Go., 1958).
26. . Ibid., sec. 150.
27. . Ibid., secs. 153, 157.
28. . Ibid., sec. 14.
29. . Ibid., sec. 199.
30. . Ibid., sec. 19.
31. . Chomsky (n. 11 above).
32. . This capacity is strictly parallel to the capacity for generating new myths or, as it amounts to the same thing, predicting the structure of as yet undiscovered myths which Claude Lévi‐Strauss claims is a central pillar in the validation of structuralist interpretation: “Either structural analysis succeeds in exhausting all the concrete modalities of its subject, or we lose the right to apply it to any one of the modalities” (“The Raw and the Cooked,” in Mythology: Selected Readings, comp. Pierre Maranda [London: C. Nicholls & Co., 1972], p. 271). For an example of him attempting to conduct just such ah exhaustive analysis see his discussion of the inverted relationship between the myth sets typical of the Sherente and Bororo Indians of Brazil. In that discussion he tries to show that on the basis of a partial knowledge of the content of a Bororo myth about the origin of water he can predict the existence of a Sherente myth which is an inversion of it (ibid., p. 286). Having found such a myth, he claims that we have witnessed a kind of contrario proof:
33. . Wittgenstein, sec. 207.
34. . H. Hartmann, Ego Psychology and the Problem of Adaptation (New York: International Universities Press, 1939), pp. 78–79; Mol (n. 20 above), pp. 206–15.
35. . Paul Ricoeur, The Symbolism of Evil, trans. E. Buchanan (Boston: Beacon Press, 1969), pp. 353, 356. Ricoeur's enterprise consists in an attempt to bridge the very real gap, or chaos, separating the worlds of professional philosophy which he feels have given up much of their rightful concern with the ontology of the sacred from the worlds of religious affirmation and religious experiences which constantly threaten to forsake a grounding in rationality. This enterprise is very similar to the one William James set himself in his The Varieties of Religious Experience ([1902; New York: Collier Books, 1961], pp. 389, 393, 401) where he again and again exclaims against the defects in a rationalism which everywhere shows its shallowing effects when not coupled with a consciousness of the “More.” Carl G. Jung, of course, and a large percentage of the so‐called third‐force psychologists who followed him, both literally and chronologically, are entirely sympathetic to James's wholism, antireductionism, and proreligiosity.
36. . Rappaport (n. 6 above), p. 71.
37. . He means to argue that because sacred propositions rarely contain material terms of specific directives and because they are usually cryptic they are difficult to falsify and contravene and hence understand (ibid., pp. 70–71).
38. . Ibid., p. 71.
39. . Albert Einstein and L. Infeld, The Evolution of Physics: From Early Concepts to Relativity and Quanta (New York: Simon & Schuster, 1938).
40. . Walter Buckley, “A Systems Approach to Epistemology,” in Trends in General System Theory, ed. George J. Klir (New York: Wiley‐Interscience, 1972), pp. 188–202.
41. . In other words, the question is, What is the source or ground of mathematical truth? Or rephrased, What is it about the empirical world that wholly nonempirical formulae (mathematical or logical propositions) can describe it accurately? Strict positivists like Rudolf Carnap argue that it is natural languages which underlie logical forms and hence they provide the ground for logical truth; others argue, with W. V. Quine, that “perhaps logical truths owe their truth to certain traits of reality” (Philosophy of Logic [Englewood Cliffs, N.J.: Prentice‐Hall, Inc., 1970], p. 95).
42. . G. J. Warnock, “John Langshaw Austin: A Biographical Sketch,” in Symposium on J. L. Austin, ed. K. T. Fann (New York: Humanities Press, 1969), pp. 3–21. Cf. J. L. Austin's discussion of the differences among “looks,”“seems,” and “appears” and how they “are not the same; and very often, where we could use one word we couldn't use another” (Sense and Sensibilia [New York: Oxford University Press, 1964], pp. 37–38). With this reminder we should approach warily the usual arguments about “appearance and reality” in professional philosophical writings whose authors have not explored the topography of these central concepts.
43. . This is especially true, of course, of romantic artists and romantic critics who felt certain that creativity and the artistic experience itself could provide revolutionary insights into the gloom of ordinary existence. See G. Bays's discussion of Arthur Rimbauds aesthetic doctrine (The Orphic Vision: Seer Poets from Novalis to Rimbaud [Lincoln: University of Nebraska Press, 1964]).
44. . Jürgen Habermas, Knowledge and Human Interests, trans. J. L. Shapiro (Boston: Beacon Press, 1972).
45. . Arnold Hauser, The Social History of Art, 2 vols. (New York: Alfred A. Knopf, Inc., 1951), 1:311–40.
46. . Messianic beliefs, conversion experiences, group pressure upon individual deviancies, and other features of the early church may be duplicated in certain ways by manipulation of ‘social environments. See Jack Brehm and Arthur Cohen, Explorations in Cognitive Dissonance (New York: John Wiley & Sons, 1962).
47. . Kenneth Lee Pike, Language in Relation to a Unified Theory of the Structure of Human Behavior, vol. 1 (Glendale, Calif.: Summer Institute of Linguistics, 1954), and With Heart and Mind: A Personal Synthesis of Scholarship and Devotion (Grand Rapids, Mich.: William B. Eerdmans Publishing Co., 1962); Marvin Harris, The Rise of Anthropological Theory: A History of Theories of Culture (New York: Thomas Y. Crowell Co., 1968).
48. . Thus Wolfhart Pannenberg concludes his study of Jesus:“…, the predestination of all things toward Jesus, their eschatological summation through Jesus, is identical with their creation through Jesus. Every creature receives through him as the eschatological judge its ultimate illumination, its ultimate place, its ultimate definition in the context of the whole creation. The essence of all events and figures is to be ultimately defined in the light of him because their essence is decided on the basis of their orientation to him” (Jesus, God and Man, trans. L. L. Wilkins and D. A. Priebe [Philadelphia: Westminster Press, 1968], p. 391).