**[[164_P3_Coherence-Stage|P3]] (Coherence):** Information ([[163_P2_Information-Stage|P2]]) must be organized. Random, incoherent information is indistinguishable from noise—effectively non-information. For information to BE information, it must exhibit **coherence**—patterns, structure, meaningful organization.
Chaos theory describes how simple deterministic rules generate complex behavior—but the rules themselves are coherent. Self-organization occurs in open systems with energy flow and boundary conditions. The "spontaneous" order emerges from the coherence already present in the laws of physics. [[164_P3_Coherence-Stage|P3]] asks: why are the laws coherent? The regress terminates in the Logos as the source of lawful coherence. Self-organization is manifestation of [[164_P3_Coherence-Stage|P3]], not refutation.
Boltzmann brain scenarios are self-undermining: if you are a Boltzmann brain, your memories are random fluctuations—you have no reason to trust your reasoning, including the reasoning leading to Boltzmann brain hypothesis. Moreover, the Boltzmann brain calculation assumes pre-existing coherent physics (thermodynamics, probability theory). The framework of statistical mechanics is itself coherent. We explain coherence by assuming coherence—circular. [[164_P3_Coherence-Stage|P3]] asserts coherence is primitive.
While specific pattern recognition is observer-relative, the existence of compressibility ([[029_D4.1_Kolmogorov-Complexity|Kolmogorov complexity]]) is objective. A random string is incompressible regardless of who compresses it. A patterned string has a shorter description regardless of who finds it. The quantitative measure C is observer-independent; the qualitative interpretation may vary. Coherence as compressibility is mathematically objective.
Correct—Shannon's entropy is syntactic, not semantic. But [[164_P3_Coherence-Stage|P3]] bridges the gap: syntactic coherence (compressibility, pattern) is the necessary condition for semantic content. Meaning cannot emerge from pure noise. Semantic information presupposes syntactic structure. [[164_P3_Coherence-Stage|P3]] establishes the structure; meaning emerges through the observer ([[162_P1_Consciousness-Stage|P1]]) interpreting that structure. Shannon is compatible with [[164_P3_Coherence-Stage|P3]]; [[164_P3_Coherence-Stage|P3]] extends Shannon toward semantics.
Quantum coherence (superposition) and [[164_P3_Coherence-Stage|P3]]-coherence (pattern/structure) are related but distinct. Decoherence destroys superposition but creates classical correlation—a different form of structure. Quantum coherence collapses into classical coherence. The total coherence picture includes both quantum and classical regimes. [[164_P3_Coherence-Stage|P3]] asserts structure at whatever level of description is relevant. Decoherence is a transition between coherence types, not destruction of coherence tout court.
Second Law:
Entropy increases in isolated systems—coherence naturally degrades. This makes coherence precious and requires explanation.
Free Energy:
Systems minimize free energy. At low T, energy minimization dominates (crystal formation = coherence). At high T, entropy maximization dominates (gas = low coherence).
Non-Equilibrium Thermodynamics:
Living systems maintain coherence by dissipating entropy:
Internal entropy decreases (coherence increases) by exporting entropy to environment.
Kolmogorov Complexity:
Coherence Definition:
Coherence = fraction of string that is compressible. C_K = 1 for perfectly patterned strings; C_K \to 0 for random strings.
Incompressibility Theorem:
Most strings are incompressible: |{x : K(x) < n-c}| < 2^{n-c}. Coherent strings are rare—structure is special.