[02] Disinformation Dynamics: Recursive Harmonics

2.1 Coherence as a Function of Recursion

Every communication system is recursive. It consists of elements that transmit signals influencing their own subsequent states. This self-reference produces coherence. A message gains meaning not because it exists but because it is repeated, referenced, and reinterpreted.

Without recursion, meaning is static. With recursion, meaning becomes dynamic and systemic, continuously regenerated by feedback. The extent to which a system reuses its own output as input—its recursivity (R)—determines its stability and adaptability.

Disinformation hijacks this self-referential loop. It injects signals that appear native but carry a slight phase offset in timing or framing, causing the system to reinforce an altered version of itself.

—

2.2 The Harmonic Basis of Systems

All systems can be described as ensembles of oscillators—entities that vary cyclically in time. Oscillations can be electrical, economic, linguistic, or emotional.

When oscillators interact, they influence each other’s timing. If coupling is weak, they remain independent. If coupling passes a threshold, they synchronise.

Synchronisation, described by Kuramoto (1984), can be understood as entrainment: the natural alignment of interacting rhythms.

The collective state of synchrony is summarised by an order parameter, which condenses the field of interactions into two values:

r: the magnitude of coherence (0 = noise, 1 = synchrony)

ψ: the shared phase or orientation of the system

These parameters describe not only physical systems but also shared attention, consensus, and collective emotion. They are both descriptive and operative. The global rhythm feeds back to influence the local dynamics, forming a control plane linking micro-behaviour and macro-order.

—

2.3 Recursivity and the Control Plane

Recursivity measures how much of a system’s present is generated from its past. In communication, it measures how strongly today’s discourse derives from yesterday’s—not by content but by relational pattern: timing, connectivity, and tone.

Mathematically, recursivity is the shared information between current and prior states divided by total information. High R means the system reproduces itself; low R means it drifts in novelty.

A balanced system maintains moderate R. High values create echo chambers; low values dissolve coherence.

The order parameter determines this balance. Rising r tightens coupling and raises R; falling r loosens coupling and reduces R. The global rhythm regulates the self-referential depth of the system.

—

2.4 The Recursion Kernel

Every system has a recursion kernel (ℛ)—the subset of interactions that maintain its identity. Outputs feed directly into inputs, preserving continuity.

In networks, the recursion kernel may appear as high-activity clusters—individuals, institutions, or algorithms whose loops dominate the discourse. In cognition, it is a neural attractor.

The recursion kernel stabilises the system but also defines its vulnerability. When compromised, coherence redirects toward alternate attractors.

—

2.5 Entropy and Adaptation

Entropy represents uncertainty and diversity. Systems must process entropy to remain alive. Too little entropy produces rigidity; too much leads to incoherence.

Disinformation destabilises this equilibrium:

Over-synchronisation: excessive alignment and suppression of diversity.

Over-randomisation: saturation by contradictory signals.

Interdiction restores the entropy balance—introducing noise to counter lock-in, or stabilisation to counter fragmentation.

—

2.6 Ontology of Data and Meaning

In this model, data are not static objects but states in a continuous field. Each communicative act possesses:

Phase: its timing within discourse

Amplitude: its emotional or attention intensity

Frequency: its recurrence rate

Coupling: its degree of mutual influence

Meaning emerges from correlation among these dimensions. It is an activity: how signals alter the field.

Disinformation acts as a phase perturbation, steering the field’s coherence through manipulation of these relationships.

—

2.7 Political Systems

Politics operates as a recursive field. Policy produces reaction, which reshapes policy. Coherence that rises too quickly produces closure—populism, autocracy, ideological rigidity.

Autocracies preserve coherence through enforced synchrony (high r, high R, low entropy). Democracies sustain adaptability through managed dissonance (moderate r and R, higher entropy).

The difference is structural, not moral. Systems suppressing noise for order lose resilience; those circulating uncertainty adapt.

—

2.8 Psychological Dynamics

Human cognition seeks synchrony. Emotional and linguistic entrainment stabilise perception and belonging. Insecurity amplifies coupling; individuals align more tightly when uncertain.

Disinformation exploits this by supplying synthetic coherence—feedback loops of affirmation that substitute rhythm for truth.

Resilience arises from reintroducing controlled asynchrony and diversity, allowing systems to breathe.

—

2.9 Recursive Harmonics as Universal Model

Across physical, biological, and social systems, persistence depends on harmonic balance between order and variation.

Recursive harmonics describes this universal architecture: oscillatory self-reference generating stability.

Harmonics denotes the structured frequencies of interaction.

Recursion denotes feedback sustaining these structures.

Systems exist as patterns of oscillating reference, not as static entities. Communication, cognition, and governance share the same substrate.

—

2.10 Summary

Coherence arises from recursion: the present regenerating the past.

The order parameter summarises and regulates coherence through a control plane.

Disinformation manipulates coupling, phase, and entropy balance to redirect coherence.

Interdiction acts on rhythm, topology, and diversity rather than on semantic content.

Stability results from sustained variation within recursive limits: coherence without closure.

[00]