Part 2: From Mandelbrot to Davos—The Geometry of Regime Change and the Pole of Loss
- john raymond
- Jan 21
- 6 min read
Part One argued something simple and stubborn: regimes do not collapse in a straight line. They bend. They absorb stress. They look stable—until the last small step flips the classification and everything changes at once. The Mandelbrot set is the cleanest mathematical picture of that fact: wide interiors of stability separated by sharp, treacherous boundaries where a tiny movement changes the outcome.
This is Part Two.
The claim here is that what Mark Carney did at Davos is not mere rhetoric. He named the boundary we have already crossed. And once you see regime change as geometry—stable lobes, fractal edges, discontinuous labels—the correct strategic posture stops being nostalgic and becomes minimax: map the ruin states, back away from them, and build the capacity to enforce the principles you claim to hold.
In short: the post–Cold War order was a regime. It has reached its boundary. If we keep pretending we are still inside the old lobe, we will drift into (Part Zero) the Pole of Loss.
I. The Mandelbrot Lesson, Re-stated as a Rule of Reality
In Part One, I used the Mandelbrot set as a regime map.
Inside the lobes, orbits settle. The behavior is compressible. You can summarize it. You can predict it. The regime label stays the same across large regions.
At the boundary, that compressibility fails. New detail appears at every scale. Zooming does not clarify the border; it produces more border. That is why boundaries are dangerous: you can make a small move and still think you are “basically in the same place,” but you have crossed into a totally different regime.
Outside, you do not have a regime at all. You have escape.
The key translation is this: real-world regimes are defined by the persistence of a classifier.
When the classifier is discrete—stable versus collapsed, normal politics versus emergency politics, deterrence versus coercion—you do not glide smoothly between labels. You step across a boundary. The world stays continuous, but your category changes discontinuously.
That is what “slowly at first, then all at once” means when you strip away poetry. The system’s stability drains gradually; the classification flips suddenly.
II. Carney at Davos: A Boundary Diagnosis
Kurzin is right about the basic significance of Carney’s speech: it is quietly devastating because it names the moment as a rupture.
Carney does not say we are “in a challenging phase.” He says we are in the midst of a rupture, not a transition. He does not say “rules-based order” as a prayer. He says: stop invoking it as though it still functions as advertised. Call the system what it is: intensifying great-power rivalry, with economic integration used as a weapon.
That is not a policy opinion. That is a regime identification.
In Mandelbrot language, Carney is saying: we are not deep in a stable lobe anymore. We are near the edge. The old summary no longer compresses reality. And if we keep trying to run the old model, we will interpret boundary behavior as “surprising events” rather than as the predictable consequence of being at the boundary.
The most useful line in the speech is the one that forces discipline on middle powers: if you are not at the table, you are on the menu. That is a statement about structural vulnerability, not moral posture.
It says: when great powers return to coercion, the “in-between” countries must either combine or be negotiated down into subordination, one bilateral concession at a time.
This is why “nostalgia is not a strategy” is not a clever headline. It is a boundary warning. Nostalgia is a refusal to update the classifier.
III. The Upgrade: From “Principled Pragmatism” to Minimax Discipline
Kurzin’s phrase—principled pragmatism—gets the instinct right: values must be aligned with capacity; moral language must be backed by enforceable action; ambition must be bounded by political will.
But the phrase still leaves room for the most dangerous error: treating ruin states as one trade-off among many.
This is where minimax matters.
When the downside becomes terminal—capture, collapse, fatal escalation, alliance fracture that cannot be repaired—the math is brutal: you cannot balance negative infinity with finite gains. You do not “trade” with ruin. You avoid it.
That is the purpose of my Pole of Loss model. It is not a claim that geopolitics literally follows a complex function. It is a way to make the geometry of ruin visible: a terrain where many starting conditions, under repeated stress, drift toward basins of catastrophic failure.
And that is the same claim Carney is making in policy language: the system is no longer forgiving. Integration does not reliably moderate adversaries. Institutions do not substitute for power. Moral signaling does not compensate for weakness.
Once you accept this, the strategic question changes. It is no longer: “How do we maximize the upside of globalization?”
It becomes: “How do we stay out of the ruin basins in a coercive environment?” That is minimax.
IV. Why the Post–Cold War Order Failed as a Compressor
For most of the post–Cold War era, Western strategy depended on a compression story:
Trade will moderate rivals.
Institutions will replace hard power.
Norms and legitimacy will keep moving in the same direction as prosperity.
America will remain a predictable anchor.
This story compressed reality for a time. It produced enough correct predictions to feel like law.
But a story that compresses well in one regime can fail catastrophically in another. Carney is naming that failure. And Kurzin is right to say the world has not drifted gently into disorder; it has hardened.
In my language: the parameter moved. The stable region shrank. The ridge deformed. The old classifier started mislabeling boundary behavior as “aberration.”
That is how regimes die: not when reality becomes incoherent, but when the ruling summary stops compressing the system accurately and leaders keep using it anyway.
V. The Missing Variable Too Many Analysts Refuse to Say
There is one factor that turns “hardening” into a cliff: internal sabotage.
In the alliance context, this is the Byzantine Traitor-General problem. External enemies are dangerous, but internal betrayal is structurally decisive.
It is not an insult to say this. It is a modeling requirement.
Since 2016, the United States ceased to be a stable constant in the European security equation. Under President Trump, coercion, transactionalism, and alliance strain are no longer hypothetical. They are active variables.
If you model the system as though reliability can be assumed, you are doing mathematics on the wrong map.
You are pretending you are still in the old, stable lobe.
VI. What the Mandelbrot Boundary Looks Like in Geopolitics
What does it look like, operationally, when a system is near its regime boundary?
It looks like what Carney describes: tariffs as leverage, integration as coercion, selective application of rules, credibility overtaking rhetoric, middle powers forced into competitive overcompliance, and bilateral negotiations that mimic sovereignty while accepting subordination.
It also looks like what everyone feels but many refuse to say: the West’s old comfort assumptions have become liabilities. The “rules-based order” sign in the window becomes a tell.
At the boundary, small moves matter.
A single announcement, a single threat, a single election, a single concession can reclassify the system from “stable competition” to “coercive hierarchy.”
This is not me being melodramatic. This is how discrete regime labels behave near a fractalline edge.
VII. The Practical Meaning of “Principled Pragmatism” Under Minimax
So what does disciplined, non-nostalgic strategy require?
It requires naming reality, as Carney insists.
It requires acting consistently, applying standards to allies as well as rivals, because selective morality is itself a vulnerability.
It requires building coalitions that work issue by issue, because relying on diminished institutions while pretending they are not diminished is another form of denial.
It requires restoring the domestic foundations that make outward strategy sustainable: industrial capacity, public trust, cohesion, and the ability to absorb shocks without political collapse.
And above all, it requires refusing to treat ruin as negotiable.
If you can see the Pole of Loss on the map, you do not keep walking toward it because the view is familiar. That path leads to death and madness.
So Where That Leaves Us?
Part One used the Mandelbrot set to make regime geometry visible: stable interiors, sharp boundaries, and sudden classification flips after long periods of stress absorption.
Part Two applies the same lens to the strategic rupture Carney described at Davos. The post–Cold War order is not gently evolving. It has reached a boundary. The old story no longer compresses the world. And when leaders keep operating as though it does, they do not “manage change.” They drift toward ruin, toward infinite loss.
That is why nostalgia is not a strategy.
And that is why principled pragmatism must be understood as minimax discipline.
We do not get to choose whether the world has hardened.
We only get to choose whether we adapt before the boundary does what boundaries always do: change everything all at once.
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