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OODA loop thinking is surprisingly hard to model mathematically (I've tried), in part because they are naturally somewhere between discrete and continuous.
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One way to see why is to ask: why hasn't game theory been properly used in OODA style analysis? The answer is that game theory doesn't offer a rich enough temporal expressivity. Discrete game theory happens in synchronized time (either simultaneous move or alternating move)
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Otoh, continuous time game theory, or differential game theory, uses continuous differential equations as the system model. For example in missile avoidance optimal maneuver planning (or dodging a defender in soccer with a feint).
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The weak example I use in my OODA workshop to get at this point is superchess: you can make 2 moves for opponent's 1, but have only a king and 4 pawns. At least initially, among experts, the 2x tempo player has a decisive advantage. But this is not quite right.
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It is a degenerate case because it is still low-integer-multiple harmonics. This can generate the "faster tempo" examples, but not the more interesting cases of getting inside opponent's OODA loop by operating *slower* than them.
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What you want is 2 things: a temporality "interference" between basic tempos, so that one party's behavior appears in an "aliased" form to the other. It's not entirely chaotic, but predictable in a disorienting way that makes you doubt your own behaviors.
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And second, a kind of tiny, hyperlocal network effect that is positive (compounding advantage) for you, negative (controlled collapse of behaviors and psyche) for the adversary. This is the "integrator" dynamic.
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What collapses adversary’s thinking is trying to model your behavior at their own tempo periodicity T1 instead of yours at T2. The lowest *rational* ratio T1/T2 determines cognitive load on them. Complexity ~ T1+T2. They get caught up in epicycles, while you’re doing ellipses.
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