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COMPLEXITY AND NATIONAL SECURITY

COMPLEXITY AND NATIONAL SECURITY. Peter Purdue & Donald Gaver Naval Postgraduate School Monterey, CA USA. COMPLEXITY AND NATIONAL SECURITY. Defense debate today Chaos Complexity Warfare Final observation on Newton. COMPLEXITY AND NATIONAL SECURITY. New, difficult defense issues

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COMPLEXITY AND NATIONAL SECURITY

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  1. COMPLEXITY AND NATIONAL SECURITY Peter Purdue & Donald Gaver Naval Postgraduate School Monterey, CA USA

  2. COMPLEXITY AND NATIONAL SECURITY • Defense debate today • Chaos • Complexity • Warfare • Final observation on Newton

  3. COMPLEXITY AND NATIONAL SECURITY • New, difficult defense issues • Effects-based operations (EBO) • Less attrition emphasis • “small” inputs may cause great outcomes: • Psychological, financial pressures effective • C3I systems • Complexity induced by many technological and human elements involved: – Facility overloading/saturation, e.g., by decoys and false targets – Hacking/jamming

  4. COMPLEXITY AND NATIONAL SECURITY • New, difficult defense issues • Land combat • Augmentation and modernization of Lanchesterian modeling • Digitization of battlefield (pros and cons) • Smart, mobile mines • ISAAC, MANA, EINSTEIN etc. • Force structure • Above plus organizational management changes: • Toward “horizontal,” “local,” “swarming” structure • Adaptive threats • Critical Infrastructure problems • Power grid

  5. COMPLEXITY AND NATIONAL SECURITY • Problem solving • Selective search over large sets of possibilities • Complex ill-defined goals • Nature of problem changes as it is explored • Computational complexity • Analogies • Metaphors • Uncertainty: deterministic and stochastic • Complex systems theory!

  6. COMPLEXITY AND NATIONAL SECURITY • Complexity and Complex Adaptive Systems (CAS). • Large number of interacting elements; non-linear, non-proportionate responses • Structure spanning several time and space scales • Capable of emerging behavior • Interplay between chaos and non-chaos • Interplay between cooperation and competition • Fitness landscapes • Co-evolution • Entropy & thermodynamics • Self-organized criticality

  7. COMPLEXITY AND NATIONAL SECURITY • Complex Adaptive Systems (CAS) • Modeled with Agent-Based Models • Rules of interaction between agents • Possible use of game theory • Bounded rationality • “Experimental Mathematics” • Distillations • Complexity • Dynamical systems and chaos • Complex systems

  8. COMPLEXITY AND NATIONAL SECURITY • Deterministic Dynamics • Difference Equations or Iterative Maps • Linear Solution Behaviors: • constant, growth/decay, oscillation. Fixed points, (stable “attractors”; unstable equilibria). • Non-Linear equations • Quadratic • “Logistic” population growth; other non-linear equations; • possible chaos: sensitive dependence on initial conditions (bounded but “unpredictable” solutions; predictable over few time steps, but later diverge; behavior is deterministically random).

  9. Deterministic Dynamics • Dynamical system equations dxi/dt = Fi(x1, x2, x3,…, xn), i = 1, 2, …n Unique Solution under mild constraints and given initial Conditions Deterministic solutions Distinct phase-space trajectories cannot cross Trajectory cannot intersect itself Attractors: bounded sets of points to which trajectories converge

  10. Deterministic Dynamics • Complications! CHAOS • Sensitive dependence on initial conditions • Errors in fixing initial position explode exponentially • Not a new observation • Tight confinement of trajectories to attractor • Also true for difference equations • Easier to illustrate with simple example

  11. The Logistic Equation: X(n+1) = 1.0X(n){1 – X(n)}, X(0) = 0.1

  12. Equation: X(n+1) = 2.0X(n){1 – X(n)}, X(0) = 0.1

  13. Equation: X(n+1) = 3.0X(n){1 – X(n)}, X(0) = 0.1

  14. Equation:X(n+1) = 3.2X(n){1 - X(n)}, X(0) = 0.1

  15. Equation: X(n+1) = 3.5X(n){1 – X(n)}, X(0) = 0.1

  16. Equation: X(n+1) = 3.55X(n){1 – X(n)}, X(0) = 0.1

  17. Equation: X(n+1) = 3.58X(n){1 – X(n)}, X(0) = 0.1

  18. Equation: X(n+1) = 3.7X(n){1 – X(n)}, X(0) = 0.1

  19. Equation: X(n+1) = 3.75X(n){1 – X(n)}, X(0) = 0.1

  20. Equation: X(n+1) = 3.8X(n){1 – X(n)}, X(0) = 0.1

  21. Equation: X(n+1) = 4.0X(n){1 – X(n)}, X(0) = 0.1 Is this RANDOMNESS?

  22. Interesting relationship X(n+1) = 4X(n){1 - X(n)} Let X(n) = Sin2πY(n), To get: Y(n+1) = 2Y(n) (mod 1) Then: Y(n) = 2nY(0) (mod 1)

  23. Interesting relationship A simple view of Y(n): Let Y(0) = .1110000101011001011….. Then: Y(1) = .110000101011001011….. Y(2) = .10000101011001011….. Y(3) = .0000101011001011….. Rule: shift sequence one step to the left at each iteration and drop off left-most digit. The process simply transforms the randomness (missing information in Y(0) into the randomness of the orbital set of Y(n). Chaos is deterministic randomness! Prediction????

  24. Deterministic Dynamics • How do we know if a system is chaotic? • Theoretical approach • Examine the equations that govern the system if they are known • Lyapunov exponent • Empirical • Examine a time series of system values • Statistical approach • Algorithmic Information Theory; Process vice Product

  25. COMPLEXITY AND NATIONAL SECURITY • Chaotic ideas • Sensitivity to initial conditions • Deterministic “randomness” • Attractors & strange attractors: • Lyapunov exponents (measure the rate at which nearby orbits diverge) • Perfectly predictability given perfect knowledge of the initial conditions • Predictability over a short time span always possible

  26. COMPLEXITY AND NATIONAL SECURITY • Beyond chaos is complexity! • What is complexity • Why do we worry about it? • If we do worry about it how do we handle it?

  27. COMPLEXITY AND NATIONAL SECURITY • Complex systems • Systems composed of many interacting parts or agents each of which acts individually but with global impact • Demonstrate self-organization and emergence • Are adaptive and co-evolve • Are responsive to small events • What does all this mean?

  28. COMPLEXITY AND NATIONAL SECURITY • Complex systems behavior • Regular and predictable under certain conditions • Regularity and predictability is lost under other circumstances • We cannot determine when the system will change phase by just examining the individual parts of the system

  29. COMPLEXITY AND NATIONAL SECURITY • Complex systems show 4 classes of behavior • Class I: Single equilibrium state • Class II: Equilibrium oscillating “randomly” between 2 or more states (temporary equilibria) • Class III: Chaotic behavior • Class IV: Combination of I, II, & III • Extended transient states but subject to “random” destruction • Power law behavior

  30. COMPLEXITY AND NATIONAL SECURITY • Business & Defense environments • Live in Class III or Class IV environment? • Class IV represents being “poised on the edge of chaos” • What happens as the level of “turbulence” increases? • Class III implies no long term strategic planning • Supports short term predictions

  31. COMPLEXITY AND NATIONAL SECURITY • Long term planning and complex systems • Class I systems are trivial to handle • Class III systems show chaotic behavior and long term predictability is virtually impossible • Class IV systems are operating ‘at the edge of chaos”: long periods of stability broken by events that drive system into Class III

  32. COMPLEXITY AND NATIONAL SECURITY • Planning in Class IV systems • A plan should not be a closed-form solution but an open architecture that maximizes evolutionary opportunities • Planning is solution by evolution rather than solution by engineering! • Not worth the effort to try to find the perfect plan or reach the perfect solution • Satisfice, not optimize

  33. COMPLEXITY AND NATIONAL SECURITY • As the level of “turbulence” increases Class IV systems move from being type II to type III • Organizations should then move resources away from trying to predict future states to learning new adaptive behaviors • (Steven Phelan) • Defense issue: how to “drive opponents chaotic” while being self-protective. • How to recognize true opponent chaos? • How to recognize, and avoid own (Blue) chaos?

  34. COMPLEXITY AND NATIONAL SECURITY • What is war? • Far from equilibrium, open, distributed, non-linear dynamical system, highly sensitive to initial conditions and characterized by entropy production/dissipation and complex, continuous feedback • An exchange of matter, information, and especially energy between open hierarchies • A complex distributed system • A Class IV system?

  35. COMPLEXITY AND NATIONAL SECURITY • What does chaos/complexity mean for warfare? • Implies that long-term planning may be very difficult in non-linear deterministic systems • Is warfare a chaotic/complex system? A number of authors seem to think so • But I find little evidence of attempts at specifying the “system” in terms of non-linear equations • Perhaps as metaphors?

  36. COMPLEXITY AND NATIONAL SECURITY • What should planners do? • Develop an adaptive stance • Be prepared to react to unexpected and unanticipated events • Develop “organizational learning” • Gain competitive advantage by adapting to novel and unpredictable situations faster than your competition. • Or, at least that is what is recommended in some of the management literature!!

  37. COMPLEXITY AND NATIONAL SECURITY • Final comment • In examining the “chaotic” nature of warfare it is not sufficient to stop at the level of suggestions, observations, and verbal arguments • The burden of proof is to uncover the dynamical equations that govern the system and to find the “strange attractors”

  38. The comments of Joseph Ford, Physics Georgia Tech • Newtonian Dynamics has been dealt a lethal blow • Relativity eliminated the Newtonian illusion of absolute space and time • Quantum theory eliminated the Newtonian dream of a controllable measurement process • Chaos eliminates the Laplacian fantasy of deterministic predictability • “The true logic of this world is in the calculus of probabilities” (Maxwell)

  39. Sources and references • Baranger, M. “Chaos, Complexity and Entropy” MIT - CTP- 3112 • Carlson, J.M. and Doyle,J. “Highly optimized Tolerance: A mechanism for Power Laws in Designed Systems”, Physical Review, E, 60, 1412 - 1427. • Ford, J. “How Random is a Coin Toss?” Physics Today, 36 (4), 40 - 47.

  40. Sources and references • Pigliucci, M. “Chaos and Complexity: Should we be Skeptical?” Skeptic, 8, 62 - 70 • Phelan, S. “From Chaos to Complexity in Strategic Planning” Presented at 55th Annual Meeting of the Academy of Management, 1995 • Rosenhead, J. “Complexity Theory and Management Practice” London School of Economics Working Paper, 1998

  41. Sources and references • Roske, V. “Opening Up Military Analysis: Exploring Beyond the Boundaries” Phalanx, 35 (2), 1 - 8. • Schmitt, J. “Command and (Out of) Control: The Military Implications of Complexity theory” in Complexity, Global Politics, and National Security, Alberts and Czerwinski, Ed. NDU Press, 219 - 246.

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