A1.3 — Information Primacy

Chain Position: 3 of 188

Assumes

A1.1 (Existence) - Something must exist
A1.2 (Distinction) - Distinguishability is the precondition for information

Formal Statement

Statement: Distinguishability IS information; therefore information is ontologically primitive.

UUID: [3be01ba9-330f-4038-957e-3b03bf294fc1]

Justification: Matter and energy reduce to informational patterns; information cannot reduce further.

Equation: H(X) = -Σ p(x) log p(x) — Shannon entropy as fundamental measure

Supporting Theories:

Shannon Information Theory (#7)
Digital Physics (#15): Universe state = finite information
Planck Black-Body (#24): E = hν — quantized information
Wheeler’s “It from Bit” (#11)

Domain Manifestations:

Domain	Expression
Physics	”It from Bit” — Wheeler
Information Theory	Information is physical — Landauer
Finance	Price = information
Psychology	Mind = information processing
Theology	”In the beginning was the Logos” (John 1:1)

Enables

D1.1 (Information Definition) - Formal definition of information
D1.2 (Bit Definition) - The minimal unit of distinction
LN1.1 (Matter-Energy Derivative) - Matter/energy supervene on information
LN1.2 (It-From-Bit) - Wheeler’s principle formalized
A2.1 (Substrate Requirement) - Information needs grounding
The entire χ-field framework depends on this

Defeat Conditions

To falsify this axiom, one would need to:

Show a property of matter/energy that is NOT informational
Define “matter” without recourse to its informational properties (mass, charge, spin, position)
Explain quantum mechanics without information theory

No successful attempt has been made.

Explanatory Frameworks & Perspectives

Perspective 1: Non-Theistic Metaphysical Realism (OPP-W)

“Information (distinguishability) is indeed more fundamental than classical matter/energy. However, this informational structure is a brute, self-existing feature of the universe. It does not imply a personal ‘Logos’ or a ‘Speaker’; it is simply the structural matrix of reality.”

Theophysics Assessment: This is a highly resilient alternative. It accepts the scientific primacy of information while rejecting the theological inference. The tension point here is whether an informational structure can be “self-grounding” (A2.2) or if “information” inherently implies a semantic, and thus personal, source.

Perspective 2: Eliminative Physicalism

“Information is a secondary, abstract property used to describe the arrangements of fundamental physical fields. Only the fields truly exist.”

Theophysics Assessment: This view struggles with 21st-century physics (e.g., Holographic Principle, Landauer’s Principle) which treats information as a physical, measurable, and conserved quantity. To call it “secondary” often requires redefining the “fundamental fields” using the very informational parameters (spin, charge) one seeks to demote.

Perspective 3: Structural Realism

“What exists are the relations and structures (information), not the objects themselves.”

Theophysics Assessment: This strongly affirms A1.3. It aligns with the framework’s claim that information is the primitive. The primary difference is whether these structures are personal/relational (Logos) or impersonal/mathematical.

Comparative Explanatory Assessment

The primacy of information is a shared conclusion of both the Theophysics framework and modern non-theistic structural realism. The divergence is not in the data (physics proves information is primary), but in the metaphysical terminus.

Theist Unification (Logos Model): Information is seen as inherently semantic and relational. If reality is “spoken” (Logos), then the informational nature of matter is a direct reflection of its source. This provides a unified explanation for why the universe is intelligible to conscious observers.
Non-Theist Realism (OPP-W Model): Information is seen as the “brute structure” of reality. The universe is a self-existing informational complex. This model is more parsimonious (no God required) but leaves the origin of the specific informational “blueprint” and its intelligibility as a brute fact.
Resilience Test: Both models satisfy the physics of A1.3. The Theophysics model gains resilience in its ability to bridge from information to consciousness (A10.1) and morality (A11.1), while the Non-Theist model maintains a lower “ontological cost” by stopping at the structure itself.

Synthesis: A1.3 does not, by itself, “convict” the materialist, but it forces any resilient worldview to account for the “It from Bit” transition. The Theophysics framework proposes that the Logos identity is the unique closure that makes this transition necessary rather than accidental.

Collapse Analysis

If A1.3 fails: The entire project of “Theophysics” (which relies on the χ-field as an informational substrate) collapses. Furthermore, any physical theory relying on the Holographic Principle or Landauer’s Principle would require radical revision.

Physics Layer

Quantum Information Revolution

The 20th-century revolution: physics IS information processing.

Quantum state = information carrier: |ψ⟩ ∈ H is not a “thing” but a description of what we can predict. The Copenhagen interpretation makes this explicit: the wavefunction is epistemic (knowledge-encoding), not ontic (stuff-encoding).

Measurement = information extraction: Observable A acting on |ψ⟩ yields eigenvalue a with probability |⟨a|ψ⟩|². This is information transfer from quantum system to observer.

Entanglement = information correlation: |Ψ⟩ = |↑↓⟩ - |↓↑⟩ encodes correlation without transmitting any physical substance. Bell violations prove this correlation exceeds classical information limits → quantum information is primary.

Holographic Principle

Bekenstein bound (1981): $S \leq \frac{2 π k _{B} RE}{ℏ c}$ Maximum entropy (information) in a region is proportional to surface area, not volume.

Bekenstein-Hawking entropy (1974): $S_{B H} = \frac{k _{B} A}{4 ℓ _{P}^{2}}$ Black hole entropy = information content = area/4 in Planck units. The information IS the black hole.

‘t Hooft & Susskind (1993): Holographic principle—a volume of space is fully described by information on its boundary. The universe is an information hologram.

AdS/CFT correspondence (Maldacena 1997): A gravitational theory in d+1 dimensions = a quantum field theory on d-dimensional boundary. Spacetime itself emerges from entanglement entropy (ER=EPR conjecture).

Landauer’s Principle (1961)

Information erasure has physical cost: $Δ Q \geq k_{B} T ln 2$ Erasing one bit dissipates at least k_B T ln 2 energy as heat. Information is physical.

Experimental confirmation: Demonstrated in 2012 (Bérut et al.) using colloidal particles. The thermodynamic cost of information is measurable.

Wheeler’s Participatory Universe

“It from Bit” (1990):

“Every it—every particle, every field of force, even the spacetime continuum itself—derives its function, its meaning, its very existence entirely—even if in some contexts indirectly—from the apparatus-elicited answers to yes-or-no questions, binary choices, bits.”

Delayed-choice experiments: Wheeler’s thought experiment (realized 2007, 2017) shows observation NOW affects which path photon took THEN. Information determines physical history.

Quantum Darwinism (Zurek)

Objective reality = redundant information: Classical reality emerges when quantum information is copied redundantly into the environment. “Reality” is information that survives decoherence.

Connection to χ-Field

If information is physically primary:

The χ-field as informational substrate becomes necessary, not optional
Matter/energy are patterns in χ, not independent substances
Consciousness (information processing) has a natural home in the ontology
The fine-tuning of physical constants becomes information selection in χ

Mathematical Layer

Shannon Information

Entropy as uncertainty measure: $H (X) = - \sum_{x \in X} p (x) lo g_{2} p (x)$

Properties that make it fundamental:

Uniquely characterized by Khinchin axioms (1957)
Additive for independent variables: H(X,Y) = H(X) + H(Y) if X ⊥ Y
Maximum for uniform distribution: H_max = log |X|
Operational meaning: optimal compression rate (Shannon’s source coding theorem)

Kolmogorov Complexity

Algorithmic information: $K (x) = min {∣ p ∣ : U (p) = x}$ K(x) = length of shortest program that outputs x on universal Turing machine U.

Why it’s fundamental:

Independent of representation (up to additive constant)
Uncomputability proves mathematical depth (information transcends mechanism)
Links to thermodynamics: S ≈ k_B K (entropy ≈ complexity)

Quantum Information Measures

Von Neumann entropy: $S (ρ) = - Tr (ρ lo g ρ) = - \sum_{i} λ_{i} lo g λ_{i}$ Generalization of Shannon to quantum states (ρ = density matrix, λ_i = eigenvalues).

Mutual information: $I (A : B) = S (A) + S (B) - S (A B)$ Quantifies entanglement and classical correlation. Can be non-zero even for spatially separated systems (quantum nonlocality).

Relative entropy: $S (ρ ∣∣ σ) = Tr (ρ lo g ρ - ρ lo g σ)$ Measures distinguishability of quantum states. Underlies quantum hypothesis testing.

Category-Theoretic Formalization

Information as functor: In FinProb (finite probability spaces), morphisms preserve information structure. The category itself encodes “what information is.”

Traced monoidal categories: Model quantum information flow. The trace operation captures feedback loops inherent in self-referential information systems (like consciousness).

Topos Theory and Logic

Internal logic of topoi: Different topoi have different logics (classical, intuitionistic, etc.). The “logic of reality” is the internal logic of the topos describing physics.

Kochen-Specker theorem in topos form: No global Boolean sections → quantum logic is fundamentally non-classical. Information structure determines logical structure.

Fisher Information

Statistical geometry: $g_{ij} = E [\frac{\partial l o g p ( x ; θ )}{\partial θ _{i}} \frac{\partial l o g p ( x ; θ )}{\partial θ _{j}}]$ Fisher metric gives Riemannian geometry on probability distributions. Information defines geometry (Amari, information geometry).

Cramér-Rao bound: $Var (\hat{θ}) \geq \frac{1}{I ( θ )}$ Information bounds measurement precision. The universe’s measurability is determined by its information content.

Source Material

01_Axioms/_sources/Theophysics_Axiom_Spine_Master.xlsx
01_Axioms/AX-003 Information Primacy.md

Term Definitions

D-002 Information
D-025 Physicalism (Materialism)
D-028 Eliminative Materialism
D-029 Nihilism

Category: Information_Theory/|Information Theory

Depends On: [ Enables: [[004_D1.1_Information-Definition](./002_A1.2_Distinction]] .md)

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