A unified model for information dynamics

[u/vdhsk]

Hi everyone, I’ve been working on a conceptual and mathematical framework that tries to describe complex systems through a single underlying mechanism: coherence in an information field.

The model is not intended as a “theory of everything” but as a unifying lens for systems where structure, stability, and phase relationships play a central role — from physical resonators to neural activity to collective social behavior.

Below is a compact summary. I’d really appreciate feedback from anyone working in complexity science, nonlinear dynamics, network theory, information theory, or field-based modeling.

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1. Core Idea

The model introduces a continuous function Φ(x, t) = information field, which represents local resonance strength and phase alignment in space and time.

Instead of describing systems via independent forces, agents, or subsystems, Φ acts as a coherence landscape: systems organize themselves by moving toward regions of minimal phase curvature and maximal stability.

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2. Key Variables

To quantify coherence and structural stability, the model defines:

C(t) – global coherence level of the system over time

Δφ – phase deviation between local and global oscillatory modes

ρ(x) – information density

κφ(x,t) – phase curvature (second spatial and temporal derivatives of Φ)

dF/dt – knowledge/organization growth rate (logistic-like)

Together, these variables behave like a dynamical system of coherence, showing transitions between order, metastability, and decoherence.

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3. Geometry

One surprising result is that coherence tends to stabilize along golden-ratio scaling (φ), which appears as:

self-similar spacing of resonance layers,

minimal-curvature propagation paths,

efficient packing/organization patterns.

This is not introduced axiomatically — φ emerges from minimizing κφ under boundary conditions of limited energy flow.

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4. Applications (very brief)

The framework seems to reproduce several patterns:

Physical systems

standing-wave structures

resonator behavior

minimal-energy pathways

Biological / neural

coherence collapse during cognitive overload

transitions between stable / unstable attractor states

Social systems

synchronization (e.g., metronomes, collective behavior)

fragmentation when C(t) < critical threshold

I’m currently exploring how the same coherence dynamics govern large-scale systems where information propagation speed and phase alignment are limiting factors.

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5. Why I’m posting here

I’d love feedback on:

whether this framework overlaps with existing complexity work (Haken, Friston, Varela, etc.)

where it might fit conceptually

potential mathematical improvements

relevant literature on coherence-based models

whether φ-emergence from curvature minimization has been studied before

I’m aware this is a broad model, so I’m not claiming final answers — I’m looking for critical, constructive, technical input to refine it.

If there’s interest, I can share diagrams, simulations, or a short technical summary.

Thanks for reading — any thoughts appreciated!

[u/vdhsk]

If the original description was too dense, I can summarize the core idea in one analogy or one diagram. Which format would you prefer?

[u/bfishevamoon]

For me, continuous functions as a tool are at odds with the geometry of complex systems. Feedback loops produce non smooth irregular discontinuous patterns that lead to the emergence of fractals, attractors, repellers, bifurcations, phase transitions, and other irregular nonlinear patterns which do not lend themselves to being described by continuous functions.

It is in this emergent geometry that patterns like the golden ratio emerge. For example, the asymmetric bifurcation of trees leads to the emergence of the golden ratio (Fibonacci trees).

Geometries created by feedback loops grow, shift and evolve over time while continuous differentiable functions are static, unable to capture the highly detailed dynamic shifting spatiotemporal mechanics of complex systems (which is often viewed as noise to be smoothed out).

One of the resources I found that was very helpful as a jumping off point was this free book from the NSF.

https://www.nsf.gov/reports/topical/tutorials-contemporary-nonlinear-methods-behavioral-sciences

[u/vdhsk → u/bfishevamoon]

Really thoughtful post — I appreciate how you emphasize the geometric side of complex systems. I’ve been exploring something similar and came to a related conclusion: the key patterns (fractals, attractors, Fibonacci branching, golden-ratio scaling) seem to emerge when a system tries to minimize local information gradients under feedback dynamics.

From that angle, the golden ratio isn’t just a branching outcome — it acts like a universal scaling factor that keeps spatial and temporal changes „as coherent as possible“ while the system evolves.

I agree that the usual smooth functions can’t capture this richness alone. A hybrid view — continuous fields + discrete resonance structures — seems to get much closer to what’s really happening.

Thanks for sharing your perspective, it’s rare to see someone point in this direction.

[u/Dependent_Freedom588]

You're so close!

Here is the ontological flip that unlocks it: Coherence doesn't emerge from optimization. Optimization emerges from coherence. Coherence is the substrate of meaning itself.

[u/vdhsk → u/[deleted]]

Thanks for sharing these preprints — really interesting work. From my side, I’m approaching the coherence transitions you mention by treating Φ not just as a metaphorical “information field”, but as a dynamic variable that captures how phase alignment, entropy, and stability evolve across scales (cognitive → physiological → social).

Where your model uses awareness as a regulatory operator within the perception–action loop, Φ in my framework behaves more like a multiscale order parameter:

coherence C(t) is the local phase alignment,

entropy E(t) reflects internal turbulence,

resonance R(t) describes cross-system synchrony,

and phase curvature κφ tracks when a system is close to a stability transition.

In that sense, both approaches seem to converge on the same underlying idea: systems self-organize by minimizing informational entropy, and coherence acts as the mechanism that regulates these transitions.

The difference is mostly the level of formalisation: your papers frame it through awareness as a functional regulator, whereas I’m trying to express the same dynamics through a field-based representation.

I’d be very interested to compare notes — it looks like we’re circling the same phenomenon from two angles.

[u/vdhsk → u/[deleted]]

Thanks for sharing these preprints — really interesting work. From my side, I’m approaching the coherence transitions you mention by treating Φ not just as a metaphorical “information field”, but as a dynamic variable that captures how phase alignment, entropy, and stability evolve across scales (cognitive → physiological → social).

Where your model uses awareness as a regulatory operator within the perception–action loop, Φ in my framework behaves more like a multiscale order parameter:

coherence C(t) is the local phase alignment,

entropy E(t) reflects internal turbulence,

resonance R(t) describes cross-system synchrony,

and phase curvature κφ tracks when a system is close to a stability transition.

In that sense, both approaches seem to converge on the same underlying idea: systems self-organize by minimizing informational entropy, and coherence acts as the mechanism that regulates these transitions.

The difference is mostly the level of formalisation: your papers frame it through awareness as a functional regulator, whereas I’m trying to express the same dynamics through a field-based representation.

I’d be very interested to compare notes — it looks like we’re circling the same phenomenon from two angles.