The 188 Axioms of Theophysics

028_A4.2_Algorithmic-Depth

4 min read

A4.2 — Algorithmic Depth

Chain Position: 28 of 188

Assumes

  • [A4.2](./027_A4.1_Parsimony]]

Formal Statement

Output complexity relative to input measures structure

  • Spine type: Axiom
  • Spine stage: 4

Spine Master mappings:

  • Physics mapping: Algorithmic Depth
  • Theology mapping: Wisdom theology
  • Consciousness mapping: Cognitive complexity
  • Quantum mapping: Quantum complexity
  • Scripture mapping: Romans 1:20 visible
  • Evidence mapping: Kolmogorov theory
  • Information mapping: Kolmogorov K(x)

Cross-domain (Spine Master):

  • Statement: Output complexity relative to input measures structure
  • Stage: 4
  • Physics: Algorithmic Depth
  • Theology: Wisdom theology
  • Consciousness: Cognitive complexity
  • Quantum: Quantum complexity
  • Scripture: Romans 1:20 visible
  • Evidence: Kolmogorov theory
  • Information: Kolmogorov K(x)
  • Bridge Count: 7

Enables

Defeat Conditions

  • Demonstrate that “Output complexity relative to input measures structure” is false, inconsistent, or inapplicable to the claimed domain.
  • Reject one of the upstream assumptions (027_A4.1_Parsimony) to collapse this axiom.

Explanatory Frameworks & Perspectives

Perspective 1: The “Simple vs. Complex” Paradox (Positivist/Skeptic)

“If the universe follows Occam’s Razor (A4.1), why is it so complicated? A universe with one electron, or a uniform gas, would be much simpler than this mess of galaxies and brains. Therefore, Parsimony is not a universal law.”

Theophysics Assessment: This objection confuses “Simplicity of State” with “Simplicity of Law.”

  • The Goal: The Logos does not seek a simple outcome (which would be boring). It seeks a simple source that generates a rich outcome.
  • The Metric: Algorithmic Depth. This is the measure of how much “work” a simple program does to produce a complex object.
  • The Distinction:
    • Randomness: High Input Complexity (incompressible), High Output. (Low Depth).
    • Triviality: Low Input Complexity, Low Output (e.g., “Print 1 forever”). (Low Depth).
    • Life/Logos: Low Input Complexity (DNA/Laws), High Output (Organism/Cosmos). (High Depth).

Perspective 2: Bennett’s Logical Depth

“The value of a structure is defined by the execution time required to generate it from its shortest description.”

Theophysics Assessment: This is the formal definition of A4.2. A “Deep” object contains evidence of a long, causal history of computation (evolution/cosmology) derived from a simple origin. The universe is “Deep” because it is 13.8 billion years of computation running on a T-shirt-sized set of laws.

Perspective 3: Creative Tension

“Complexity arises from the tension between two opposing forces: Expansion (Energy) and Compression (Gravity/Parsimony).”

Theophysics Assessment: This aligns with the Logos model. The “Father” generates potential (Expansion), the “Son” orders it (Compression/Parsimony), and the “Spirit” actualizes the Depth.

Comparative Explanatory Assessment

A4.2 explains Why there is Something Interesting rather than Something Simple.

  1. Theist Unification (Logos Model): The Logos is a “Creator,” not just a “Simplifier.” The goal of Creation is to maximize Meaning (Depth) using the most efficient means (Parsimony). This explains the specific character of our universe: simple laws, complex history.
  2. Structural Realism (Brute Depth): The universe just happens to be a system that generates depth. It’s a “Critical System” poised between order and chaos. This describes what happens but doesn’t explain why the constants are tuned to this specific critical point.
  3. Instrumentalism (Fictional Depth): We call things “Deep” because we like them. But the “Depth” (computation time) is an objective physical fact, not an opinion.

Synthesis: A4.2 resolves the tension between A3.1 (Order) and the visible complexity of the world. It defines the universe as a Generative Fractal: infinite complexity unfolding from a finite, elegant seed.

Collapse Analysis

If [028_A4.2_Algorithmic-Depth.md) fails:

  • We cannot distinguish between “Good Complexity” (Life) and “Bad Complexity” (Noise).
  • We cannot explain why the universe didn’t just stay as a uniform gas (which is simpler).
  • The concept of “Value” loses its information-theoretic grounding.

Source Material

  • 01_Axioms/_sources/Theophysics_Axiom_Spine_Master.xlsx
  • 01_Axioms/AX-005 Algorithmic Depth.md

Term Definitions

  • We cannot distinguish between “Good Complexity” (Life) and “Bad Complexity” (Noise).
  • We cannot explain why the universe didn’t just stay as a uniform gas (which is simpler).
  • The concept of “Value” loses its information-theoretic grounding.

Source Material

  • 01_Axioms/_sources/Theophysics_Axiom_Spine_Master.xlsx
  • 01_Axioms/AX-005 Algorithmic Depth.md

Term Definitions

  • **D-030 Algorithmic Depth.md)

Quick Navigation

Category: [[_WORKING_PAPERS/Information_Theory/|Information Theory**

Depends On: [← Back to Master Index](./027_A4.1_Parsimony]]

Enables: 029_D4.1_Kolmogorov-Complexity

[[_WORKING_PAPERS/_MASTER_INDEX.md)

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