"God separated the light from the darkness"
— Genesis 1:4
Bit = minimal unit of distinction (binary choice)
The Bekenstein bound proves otherwise—finite regions contain finite bits. "Infinite precision" real numbers are mathematical abstractions, not physical realities. Every measurement has finite precision. The universe is quantized at Planck scale. Continuous descriptions are approximations to underlying discrete structure.
Correct, but measurement of a qubit yields exactly one bit. The superposition |0⟩ + |1⟩ collapses to |0⟩ or |1⟩ upon observation ([[045_A6.1_Superposition|A6.1]]-[[046_A6.2_Collapse|A6.2]]). The bit is the output of quantum measurement. Qubits extend the bit; they don't replace it.
Any base-n digit is reducible to ⌈log₂(n)⌉ bits. The bit is minimal because 2 is the smallest integer > 1. Distinction itself ([[002_A1.2_Distinction|A1.2]]) is inherently binary: X or not-X. The bit captures this logical minimality.
Natural units suggest fundamental discreteness:
Bekenstein bound implies discrete information:
N_{bits} \leq \frac{2\pi R E}{\hbar c \ln 2} = \frac{A}{4 \ell_P^2 \ln 2}
Maximum bits in a sphere = area/(4 Planck areas). Information is counted in BITS, not continuous quantities.
Any integer n ≥ 0 has unique binary representation:
n = \sum_{i=0}^{k} b_i 2^i, \quad b_i \in \{0,1\}
Bit depth: ⌈log₂(n+1)⌉ bits encode integers 0 to n.
Extension to reals: Binary expansion x = Σ b_i 2^(-i) (may be infinite). Computable reals have finite K-complexity descriptions.
| Domain | Mapping |
|---|---|
| Physics | Observables / Contrast |
| Theology | Genesis 1 ordering |
| Consciousness | Qualia |
| Quantum | Quantum distinguishability |
| Scripture | Genesis 1:4 light/dark |
| Evidence | QM experiments |
| Information | Distinction as bit |
Bridge Count: 7