Almost all real numbers are random. Their binary expansions are infinite, incompressible bitstrings — sequences with no shorter description than themselves. This is the lesson of algorithmic information theory: the computable numbers we know and love (π, e, √2) are measure-zero anomalies in a sea of incompressibility. The continuum is dominated by randomness.
This sea has a name now: the Chaos Reservoir, or simply Chaos.
Chaos Reservoir
Think of the real line itself as a reservoir of infinite randomness. Each real number is a frozen sample of infinite random bits. Almost all are incompressible. Only a vanishingly small subset can be generated by a finite rule. Physics, mathematics, observers — these are coherent patterns carved out from the Chaos.
Chaos is not structureless in the trivial sense. It contains everything: every possible infinite bitstring, every conceivable pattern, every possible rule for recognizing patterns. The overwhelming majority are noise, but hidden within are islands of order.
Coherence as Filter
Why do some patterns persist as physics, logic, or conscious minds, while most dissolve into noise? The answer is coherence. Coherence acts as a filter: only structures that are self-consistent, that do not contradict themselves, can survive.
But here’s the recursion: every possible coherence filter is itself just another pattern in the Chaos. Chaos contains not only the random noise but also the algorithms, rules, and constraints that carve islands of order out of it. Coherence is not imposed from outside; it emerges from within.
Closing the Loop
This resolves the hierarchy:
Chaos — the reservoir of infinite randomness, the ocean of reals.
Coherence — patterns that self-consistently persist within Chaos.
Constructors — stable, repeatable patterns that effect transformations.
Physics — the emergent regularities describable in constructor theory.
Consciousness — coherence-aware constructors, observers of order.
In this view, Chaos is maximally self-sufficient. It contains the noise, the filters, and the filtered structures. Everything that can exist, including the rules that define what can exist, is already there.
Next Steps
This post introduces Chaos as the metaphysical foundation — the reservoir from which coherence and order are drawn. In subsequent posts, I’ll elaborate:
How coherence can be formalized as a self-extracting pattern.
How constructor theory fits on top of Chaos.
How consciousness emerges as coherence recognizing itself.
For now: Chaos is the ground. Out of it comes everything.