1 complexity and national security peter purdue & donald gaver naval postgraduate school...
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COMPLEXITY AND NATIONAL SECURITY
Peter Purdue & Donald Gaver
Naval Postgraduate School
Monterey, CA
USA
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COMPLEXITY AND NATIONAL SECURITY
• Defense debate today
• Chaos
• Complexity
• Warfare
• Final observation on Newton
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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
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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
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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!
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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
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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
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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).
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Deterministic Dynamics
• Dynamical system equations
dxi/dt = Fi(x1, x2, x3,…, xn), i = 1, 2, …nUnique 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
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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
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The Logistic Equation: X(n+1) = 1.0X(n){1 – X(n)}, X(0) = 0.1
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Equation: X(n+1) = 2.0X(n){1 – X(n)}, X(0) = 0.1
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Equation: X(n+1) = 3.0X(n){1 – X(n)}, X(0) = 0.1
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Equation:X(n+1) = 3.2X(n){1 - X(n)}, X(0) = 0.1
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Equation: X(n+1) = 3.5X(n){1 – X(n)}, X(0) = 0.1
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Equation: X(n+1) = 3.55X(n){1 – X(n)}, X(0) = 0.1
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Equation: X(n+1) = 3.58X(n){1 – X(n)}, X(0) = 0.1
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Equation: X(n+1) = 3.7X(n){1 – X(n)}, X(0) = 0.1
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Equation: X(n+1) = 3.75X(n){1 – X(n)}, X(0) = 0.1
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Equation: X(n+1) = 3.8X(n){1 – X(n)}, X(0) = 0.1
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Equation: X(n+1) = 4.0X(n){1 – X(n)}, X(0) = 0.1
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Series1
Is this RANDOMNESS?
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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)
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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????
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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
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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
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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?
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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?
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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
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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
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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
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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
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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
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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?
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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?
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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?
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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!!
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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”
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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)
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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.
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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
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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.