Doh, in hindsight obvious insight that I shoulda seen years ago. Disruption is to "get inside the adversary's OODA loop" as integration is to differentiation. The differential equation is the specific exploit by which you pwn the adversary's complacent-predictable behavior loop.
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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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A good motif of what I'm talking about is a Vernier caliper, which you may have used in high school physics lab. Where 10 divisions on the vernier scale correspond to 9 divisions on the main scale, and you can get to 1/10th resolution.
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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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