McNair Paper Number 52, Chapter 8, Notes, October 1996

1. Yves Coppens, "East Side Story: The Origin of Humankind," Scientific American, May 1994, 89 and 94-95; also, Meave Leakey, "The Dawn of Humans," National Geographic, September 1995, 41-42.

2. Rick Gore, "The Dawn of Humans: Neandertals," National Geographic, January 1996, 11-12 and 30; David Pilbeam, "The Descent of Hominoids and Hominids," Scientific American, March 1984, 96. Pilbeam puts the emergence of modern man at 40-45,000 years ago; Gore, writing a decade later, states that in the 1980s the remains of modern humans that lived at least 90,000 years ago were unearthed.

3. Charles Darwin, The Origin of the Species by Means of Natural Selection, in Great Books of the Western World, ed. Robert Maynard Hutchins, vol. 49 (Chicago: Encyclopaedia Britannica, 1952), 239. For an overview of Darwin and the theory of natural selection as formulated in The Origin of the Species, see Ernst Mayr, The Growth of Biological Thought: Diversity, Evolution, and Inheritance (Cambridge, MA: Belknap Press, 1982), 394-534. From 1859 to 1872, six editions of The Origin of the Species appeared, and Darwin vacillated a great deal throughout his life on some issues, notably speciation (ibid., 410 and 424).

4. Daniel C. Dennett, Darwin's Dangerous Idea: Evolution and the Meanings of Life (New York: Simon and Schuster, 1995), 20.

5. Richard Dawkins, The Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe Without Design (New York: W. W. Norton, 1987), 114.

6. Dennett, Darwin's Dangerous Idea, 20. Mayr, for example, is generally credited with the modern theory of speciation by initial geographical separation (Dawkins, 239).

7. Dennett, Darwin's Dangerous Idea, 19. For those whose minds are not entirely closed but nonetheless see neo-Darwinism as being substantially in doubt, Dennett's Darwin's Dangerous Idea and Dawkins' The Blind Watchmaker provide excellent overviews of the modern synthesis and the evidence supporting it.

8. Stephen Jay Gould, "The Evolution of Life on the Earth," Scientific American, October 1994, 85. In 1972, Gould and Niles Eldredge put forward a theory of punctuated equilibrium that described the pattern of biological evolution as being one of long periods of relative stasis punctuated by short evolutionary bursts in which new species emerge. This theory has been interpreted, falsely it turns out, by many outside the fields bearing on evolutionary theory as a refutation of Darwin. Gould's position in his overview of evolutionary theory for the October 1994 issue of Scientific American does not support this interpretation. For an overview of the punctuationist controversy, see Dawkins, 223-252.

9. Richard Dawkins, "Darwin Triumphant: Darwinism as a Universal Truth," in Michael H. Robinson and Lionel Tiger, eds., Man and Beast Revisited (Washington, DC: Smithsonian Institution Press, 1991), 38; also see Dawkins, The Blind Watchmaker, 317. Dawkins' claim regarding adequate explanations of adaptive complexity should not be construed as implying that core Darwinism is anything other than an empirical theory. As Dawkins has stressed, discovery of "a single, well-verified mammal skull . . . in 500 million year-old rocks" would utterly destroy core Darwinism (The Blind Watchmaker, 225). Darwin himself was equally clear about the empirical nature of natural selection: "If it could be demonstrated that any complex organ existed, which could not possibly have been formed by numerous, successive, slight modifications, my theory would absolutely break down" (Darwin, cited in Dawkins, The Blind Watchmaker, 249).

10. Richard M. Swain, "Lucky War": Third Army in Desert Storm (Fort Leavenworth, KS: U.S. Army Command and General Staff College Press, 1994), 300.

11. Ibid., 300-301.

12. The loss of focus, particularly on leadership targets, that became evident toward the end of the first week of the Desert Storm air campaign among Coalition air planners in (then) Brigadier General Buster Glosson's "Black Hole" planning cell indicates that the frictional problem Swain highlighted in the case of Coalition ground operations surfaced among airmen as well.

13. John Boyd deserves credit for reminding the author that mechanized forces such as German panzer units in May 1940 had been able to sustain offensive operations longer than four days by allowing participants to "cat nap" at every opportunity.

14. Lionel Tiger, "The Cerebral Bridge from Family to Foe," in J. Von Der Dennen and V. Falger, eds., Sociobiology and Conflict: Evolutionary Perspectives on Cooperation, Violence, and Warfare (London: Chapman and Hall, 1990), 103.

15. This formulation was consciously patterned on John Boyd's observation-orientation-decision-action "cycle" or "loop." The roots of Boyd's "OODA loop," as it is usually termed, can be traced at least back to his 4 August 1976 briefing "New Conception for Air-to-Air Combat," which stressed such ideas as achieving faster operational tempos than the adversary. Boyd first coined the term "observation-orientation-decision-action cycle" in early 1978.

16. Captain Don S. Gentile, as told to Ira Wolfert, One-Man Air Force (New York: Stratford Press, 1994), 11. Today, Gentile is officially credited with 19.83 air-to-air kills of German aircraft in Europe during World War II. However, during some of his wartime service, the U.S. Eighth Air Force also credited German aircraft destroyed on the ground as "kills." Gentile's wartime tally when he completed his last operational sortie in April 1944 was 23 German aircraft destroyed in the air and 7 on the ground [Mark M. Spagnuolo, Don S. Gentile: Soldier of God and Country (East Lansing, MI: College Press, 1986), 298].

17. Robin Fox, "Aggression: Then and Now," in Man and Beast Revisited, Michael H. Robinson and Lionel Tiger (Washington, DC: Smithsonian Institution Press, 1991), 89.

18. John Boyd had concluded by 1977 that it was the differential in friction between the two sides that mattered most in combat outcomes.

19. Newton, Mathematical Principles of Natural Philosophy, in Great Books of the Western World, vol. 34, 14.

20. Mayr, 33. In key instances in which biological and physical thought conflicted, as in William Thomson's calculation that the age of the earth had to be several orders of magnitude less than the "several thousand million years" postulated by Darwin, the biologists turned out to be right and the physicists wrong (ibid., 428). As Mayr also noted, the skepticism about evolution expressed to him by physicists as prominent as Niels Bohr and Wolfgang Pauli seems to have been based in no small part on an "oversimplified understanding of the biological processes involved in evolution" (ibid., 429).

21. For a summary of the main facts and generalizations that constituted Darwin's original theory of evolution by natural selection, see Mayr, 479-480. Illustrative of the generalizations or principles involved in natural selection is the following: "Survival in the struggle for existence is not random, but depends in part on the hereditary constitution of surviving individuals. This unequal survival constitutes a process of natural selection" (ibid., 480). For the main principles of neo-Darwinian population genetics, see Mayr, 551. An example of the qualitative principles underlying population genetics is: "There is only one kind of variation, large mutations and very slight individual variants being extremes of a single gradient" (ibid.).

22. Michael Scriven, "Explanation and Prediction in Evolutionary Theory," Science, 28 August 1959, 477.

23. Henri Poincar(, Science and Method, trans. Francis Maitland (New York: Dover, 1952), 15-24. Much the same point can be made about mathematics itself. While rapid growth computational capabilities has given rise to a kind of empirical mathematics not previously practicable, the hallmark of mathematical truth remains provability, and the ultimate criteria for what is accepted as mathematical proof remains both qualitative and subjective. An example is the intuitionist's rejection of the law of the excluded middle (p or not-p) in order to limit mathematical existence to denumerable sets, thereby eliminating the "non-intuitive" transfinite sets first explored by Georg Cantor as meaningless [L. E. J. Brouwer, "Intuitionism and Formalism," in Paul Benacerraf and Hilary Putnam, eds., Philosophy of Mathematics: Selected Readings (Englewood Cliffs, NJ: Prentice Hall, 1964), 70-71]. Logically this rejection amounted to excluding negation elimination (not-not-p implies p) as a permissible rule of inference in mathematical proofs. Few working mathematicians today embrace the position that mathematics must be bounded by our intuitions of the natural numbers. Their disinclination to do so, however, rests on historical, pedagogical, and anthropological reasons that defy clearly quantification [Philip J. Davis and Reuben Hersh, The Mathematical Experience (Boston: Birka(user, 1981), 395].

24. Stewart, Does God Play Dice? The Mathematics of Chaos, 116-118.

25. Ibid., 87.