Constructors From Coherence

In the previous post, I introduced Coherence Filters: rules that carve islands of order out of the Chaos Reservoir, the measure-theoretic sea of random reals. Coherence is not imposed from outside but emerges from within Chaos itself. Some patterns survive because they are self-consistent—they encode filters that select themselves.

Now we turn to the next step: constructors. These are not merely coherent patterns, but patterns that transform other patterns while persisting unchanged. They are the bridge from coherence to physics.

1. What is a Constructor?

Following Deutsch and Marletto, a constructor is:

“Anything that can cause transformations in physical systems without undergoing any net change in its ability to do so.” ([Deutsch, Constructor Theory, 2012])

Or equivalently:

“A constructor performs a task whenever it is presented with substrates in a legitimate input state, transforming them to the appropriate output state, while retaining its own capacity to perform the task again.”

Within the Chaos framework:

• A constructor is a self-coherent pattern that enacts a mapping between patterns in Chaos.

• The key property: it retains its ability to enact that mapping, no matter how many times it is considered.

• Formally: if F is a filter encoding a pattern ss, then ss is a constructor if it defines a relation T:C→C such that F(T(x))=1 for inputs x in some domain, while preserving F(s)=1.

2. Static Chaos, Dynamic Relations

Chaos, as defined, is static: the set of all infinite random bitstrings. Nothing “happens” in it. How then can we talk about transformations?

The resolution is that transformations are not literal changes to Chaos. Instead, they are stable correlations across subpatterns of Chaos. For example:

• A hydrogen atom is a constructor pattern that correlates input bitstrings (electron + photon) with output bitstrings (electron + photon at higher energy).

• The atom pattern persists in both input and output states. It embodies the correlation.

Thus:

• Filters define static coherence: which states are valid.

• Constructors define relational coherence: which correlations between states are valid.

3. From Filters to Constructors

A filter merely distinguishes order from noise. A constructor actively propagates coherence by defining correlations:

• Filters: static recognition — “this sequence is coherent.”

• Constructors: relational mapping — “this sequence coherently maps to that sequence.”

The transition is crucial: once coherence can propagate through correlations, order is no longer a fragile accident in Chaos. It becomes self-sustaining.

4. Fixed Points and Persistence

As with coherence filters, the constructor condition has a fixed-point character:

• A constructor ss persists if ss encodes a filter FF that both selects itself and enacts correlations that preserve FF.

• In symbols: F(s)=1F(s) = 1 and for relevant xx, F(T(x))=1F(T(x)) = 1.

This dual condition ensures:

1. Self-coherence — the constructor endures.

2. Transformational closure — the constructor propagates coherence into its environment.

5. Emergence of Physics

Physics, on this view, is the emergent layer built on constructors:

• The laws of physics are the stable constraints that determine which correlations are coherent.

• Constructors instantiate those laws by embodying the allowed correlations while retaining coherence.

• Physics is thus not a primitive backdrop but a catalogue of coherent correlations emerging from Chaos.

Example: a hydrogen atom is a constructor—it persists in its self-coherent structure and reliably correlates inputs (electron + photon) with outputs (electron + photon at higher energy).

6. Toward Conscious Constructors

Constructors bridge Chaos and physics. But the arc continues:

• Some constructors stabilize transformations of extraordinary generality (universal computers, brains).

• Consciousness may be modeled as a constructor that not only preserves coherence but represents it internally, becoming coherence-aware.

This leads to the next frontier: understanding how consciousness fits into the constructor stack.

Conclusion

The story so far:

1. Chaos Reservoir — infinite randomness.

2. Coherence Filters — self-consistent patterns that survive.

3. Constructors — coherent patterns that enact stable correlations while retaining their ability to do so.

From Chaos arises coherence, from coherence arises constructors, and from constructors arises physics. The universe is not built from atoms up, but from Chaos down, through coherence into correlation.