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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• Defense debate today

• Chaos

• Complexity

• Warfare

• Final observation on Newton

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• 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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• 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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• 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 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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• 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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• 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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• 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) = 3.2X(n){1 - X(n)}, X(0) = 0.1

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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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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.

1 complexity and national security peter purdue & donald gaver naval postgraduate school...

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