Phased Complexity Doctrine

Phased Complexity Doctrine

Axiom

Systems do not grow linearly.
They thicken in phases.

Doctrine

This doctrine holds that complexity accumulates in discrete phases rather than smooth, predictable increments. Early additions create minimal drag, but each subsequent layer interacts with those beneath it, accelerating entanglement. As systems mature, small changes generate disproportionately large downstream effects because dependency density increases, coupling tightens, and shock absorption diminishes.

Complexity follows a curve—slow, then rapid, then unstable. Treating complexity as linear leads to chronic miscalculation; recognizing its phased behavior enables accurate forecasting, restraint, and earlier intervention before fragility steepens.

Within Convivial Systems Theory, the Phased Complexity Doctrine explains why systems appear stable for long periods and then fail suddenly: the system crossed a phase boundary, not a tolerance margin.

Form

Phase I: Low drag
Phase II: Coupling increases
Phase III: Fragility steepens

Neural Network Mapping

(Phase transitions in layered systems)

In learning systems, phased complexity appears as depth and interaction grow faster than interpretability. Early layers add capability with little cost. As architectures deepen, interactions multiply, gradients entangle, and small parameter changes produce large behavioral shifts.

Late-phase models become sensitive to minor perturbations. Training instability, brittle generalization, and opaque failure modes emerge not because the system is “too complex,” but because it crossed a coupling threshold.

In ML terms:
depth compounds non-linearly.
phase boundaries—not parameter counts—determine fragility.

Effective design recognizes these transitions and favors restraint before interpretability collapses.

Applied example (SIA)

Why LED Speed Signs Create New Hazards (Systems in Action)