Axiom · Chain Position 27 of 346

PARSIMONY

**Statement:** Nature prefers minimal description.

Connections

Assumes

  • None

Enables

  • None
Physics Layer

Action Principles

Hamilton's Principle: The path taken by a physical system extremizes the action:

S = \int_{t_1}^{t_2} L(q, \dot{q}, t) \, dt

The actual path minimizes (or extremizes) S. This is parsimony: nature takes the "shortest" path in configuration space.

Fermat's Principle: Light takes the path of least time. Parsimony in optics.

Feynman Path Integral: All paths contribute, but the classical path dominates because it extremizes the action. Quantum mechanics enforces parsimony.

Mathematical Layer

Kolmogorov Complexity

Definition:

K(x) = \min\{|p| : U(p) = x\}

K(x) = length of shortest program that outputs x on universal Turing machine U.

Properties:

  • K(x) ≤ |x| + c (never much more than trivial encoding)
  • K(x) is uncomputable (Chaitin's incompleteness)
  • K(x|y) = conditional complexity (x given y)

Invariance theorem: K is independent of choice of U up to additive constant. Parsimony is objective, not observer-dependent.

Defeat Conditions

To Falsify This

  1. **Show nature prefers complex descriptions** — Find a physical law that is unnecessarily complicated
  2. **Demonstrate Occam's Razor fails empirically** — Show simpler theories are regularly wrong
  3. **Explain why physics is mathematical without parsimony** — Why should equations be elegant?