McNair Paper Number 52, Chapter 11, Notes, October 1996

1. Lt. Col. Ed Felker, "Information Warfare: A View of the Future," A Common Perspective: Joint Warfighting Center's Newsletter, September 1995, 18.

2. Larry Lynn, "Battlefield Dominance and ARPA Focus," Advanced Research Projects Agency (ARPA) memorandum, 29 June 1995, 2.

3. John Boyd has identified the differences or mismatches (whether large or small) that unavoidably exist between the world and our understanding of it at any point in time as the root source of novelty in science, engineering, and technology ("Conceptual Spiral," slide 23).

4. Paul Carroll, Big Blues: The Unmaking of IBM (New York: Crown Publishers, 1993), 217-222, 325-328, and 347. IBM executives had ample warning of the changes that would restructure their industry. "They commissioned months-long task forces with loads of smart people and forecasted the changes in the market that would cripple IBM, but IBMers couldn't quite bring themselves to do anything about those cataclysmic changes" (ibid., 3).

5. Andrew Marshall provided this anecdote. The Israeli intent was to use RPVs primarily to locate targets beyond friendly lines. To get there, however, the vehicles had to overfly friendly units and soon began revealing that friendly forces were often not located precisely where they claimed to be. While the RPVs were indeed used in their intended role, the Israelis felt that imposing much greater discipline on position reports by their own units constituted the larger tactical benefit.

6. "A Survey of Telecommunications: The Death of Distance," The Economist, 30 September 1995, 28.

7. Andrew Marshall suggested this possibility.

8. Richard Dawkins, The Blind Watchmaker: Why the Evidence of Evolution Reveals a University without Design (New York: W. W. Norton, 1987), 73. The basic idea of Dawkins, Fisher, and other biologists is that large leaps in animal design space have a much lower probability of being viable than small ones.

9. Martin van Creveld, The Transformation of War (New York: The Free Press 1991), ix-x, 2, 29, 62, and 224-225.

10. Ibid., 245. It is relevant, given the interpretation of Clausewitz in chapters 2 and 3, to add that van Creveld's reading on Vom Kriege is, well, odd. For instance, he asserts without any discussion or argument that Vom Kriege uses the "axiomatic method" and is "mainly deductive in character" (ibid., 35). One can only conclude that van Creveld has little familiarity with axiomatic methods, whether those of Euclid, Giuseppe Peano, Gottlob Frege, or their successors. Those interested in pursuing this particular criticism may wish to compare Clausewitz's method with that in Patrick Suppes' Axiomatic Set Theory (New York: Dover, 1972).

11. Richard Simpkin, Race to the Swift: Thoughts on Twenty-First Century Warfare (London: Brassey's Defence Publishers, 1985), 106.

12. Early versions of the second law of thermodynamics arose from studying irreversible processes in which some of the energy in a system becomes unavailable for useful work. Rudolf Clausius (1822-1888), for instance, formulated the second law as the principle that "No process is possible in which the sole result is the transfer of energy from a cooler body to a hotter body" [Peter W. Atkins, The Second Law (New York: W. H. Freeman and Company, 1984), 25]. Entropy, whose unit of measurement is energy/temperature (joules/degree Kelvin, for example), was introduced to label the manner in which energy is stored in thermodynamic systems (ibid., 38). A more modern statement of the second law is that if an isolated system in thermodynamic equilibrium has a state function, S, which is the entropy or degree of disorder of the system, then dS/dt $ 0 [GrJgoire Nicolis and Ilya Prigogine, Exploring Complexity: An Introduction (New York: W. H. Freeman and Company, 1989), 61-62]. When Boyd first connected Clausewitzian friction and the second law of thermodynamics is hard to determine precisely. However, a critique of his "Patterns of Conflict" briefing, written by a military historian following its presentation to the faculty of the U.S. Army Command and General Staff College in May 1982, confirms that he was describing friction as Clausewitz's most important contribution to military thought at that time. It was Ludwig Boltzmann (1844-1906) who related the macroscopic state of a thermodynamic system to its microscopic arrangements. Boltzmann's formulation of this relationship takes the form S = k logW, where S is entropy, k is Boltzmann's constant, and W represents the number of microscopic arrangements of the system associated with entropy S (Atkins, 65-79). In the 1940s, Claude Shannon's early work on information theory revealed that information, understood as a measure of one's freedom of choice when selecting a message, has the same form as Boltzmann's famous equation for entropy [Claude E. Shannon and Warren Weaver, The Mathematical Theory of Communication (Urbana, Illinois: University of Illinois Press, 1949), 9, 27, and 48-53]. Perhaps more than anything else, it was Boyd's appreciation of this connection between information (in the sense of uncertainty) and entropy (or disorder) that led him to connect Clausewitzian friction with the second law of thermodynamics.