Recursion in RDD: Mechanisms and Implications
Recursion in RDD: Mechanisms and Implications
This molecule elaborates on the Recursion atom, detailing the mechanisms and implications of recursion in Recursive Distinction Dynamics.
Recursion is not repetition and not self-reference by definition. It occurs when distinctions persist as records, records influence subsequent dynamics, state updates are ordered in time, and constraints and noise permit continuity rather than reset.
This note covers mechanisms, implications, and formalization. It does not introduce new primitives.
Structural Introspection
Atoms Used (Declared Dependencies)
- Recursion in RDD: Mechanisms and Implications:
- Record (Memory Substrate)
- Persistent Distinction
- Time
- Constraint
- Noise
- Existence
This list represents explicit conceptual dependencies, not incidental mentions.
Atoms Referencing This Molecule (Backlinks)
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These atoms reference this molecule but may not be foundational to it.
Atom Mentions Not Declared as Dependencies
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If an atom appears here, consider whether it should be added to atoms:.
- Internal RDD synthesis: ☐
- External alignment (physics): ☐
- External alignment (philosophy): ☐
- External alignment (neuroscience): ☐
Confidence level
- ☐ Exploratory
- ☐ Provisional
- ☐ Stable
Mechanisms
Recursion requires time, persistence, and constrained interaction.
Ontic / Core Claim
Recursion is not repetition and not self-reference by definition.
It occurs when:
- distinctions persist as records,
- records influence subsequent dynamics,
- state updates are ordered in time,
- constraints and noise permit continuity rather than reset.
Formally, recursion can be expressed as:
[
S_{t+1} = F(S_t, R_t)
]
where (R_t) denotes the record(s) carried forward from prior states.
Without records, systems evolve but do not recurse.
[!warning]+ Source Needed
- For formalization and mathematical treatment, see external sources in cybernetics and systems theory.
Distillation
Recursion is memory acting on the present.
Why it matters
- Time: Recursion depends on ordered state change.
- Existence: Persistent entities are sustained through recursive update.
- Complexity: Layered structure arises from repeated constrained updates.
- RDD coherence: Prevents circular definitions of process and state.
Conflicts
- Purely logical or abstract notions of recursion
- Accounts that treat recursion as instantaneous self-reference
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- Date: 2025-12-29
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