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QUESTION-243: Does temporal information retention track causal propagation, do the ΦID criterion Ψ and dynamical independence agree, and does either of those two detect interaction among the parts or price the size of a feature?

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Properties5
StatusAnswered
Tagsindividuation, information-theory
Linedistributed-agency
RefinesQUESTION-115 — Beyond what retention, dynamical independence and Ψ are known to track, can a collective's boundary, its temporal resolution and its macrostate be found together, by temporal information retention, dynamical independence, effective information and an Occam price on the candidate, and where these criteria disagree on one system, which level does each pick?
Answered byTHEORY-424 — Mutual-information measures of individuality that read a system's next state off its present one measure association, not propagation: I(S_{t+1}; S_t) can be positive when the environment alone drives the system, and conditioning on the environment does not recover the interventional quantity, which can be zero where the conditional measure is one bit, THEORY-764 — For a deterministic supervenient feature V of a Markov system, Rosas et al.'s practical emergence criterion Ψ equals the parts' whole-minus-sum information about V's next value minus V's one-step dynamical dependence I(V_t′; X_t | V_t), so dynamical independence raises Ψ but neither implies emergence nor is implied by it, and the paper's sufficient test for causal decoupling can pass a feature that is not dynamically independent

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Answer

No to each. This is the part of QUESTION-115 that asks where its criteria disagree and what each tracks, split off on 2026-10-21 (ADR-049).

  • Retention is association. THEORY-424 (Active), from Bourrat (2024), read in NOTE-027. Krakauer et al.’s A* = I(S_{t+1}; S_t) can be positive when the environment alone drives the system. Conditioning on the environment does not give the interventional quantity: in NOTE-027’s XOR system A = 1 bit and  = 0. Retention tracks predictive dependence, not causal propagation.
  • Ψ and dynamical independence diverge both ways. THEORY-764 (Active), the record’s derivation from Rosas et al. (2020) and Barnett and Seth. For a deterministic feature of a Markov system, Ψ is the parts’ whole-minus-sum information about the feature’s next value minus its one-step dynamical dependence. A self-copying single part is independent and not emergent. A parity whose persistence depends on one bit passes Ψ’s decoupling test and is not independent.
  • Neither detects interaction. The sum of independent identical AR(1) channels is both emergent by Ψ and independent, with no interaction at all.
  • Neither prices size. Neither Ψ nor the dependence term charges for the size of the feature, and the whole-minus-sum term can grow with the number of parts summed.

So independence tracks closure, and Ψ tracks closure plus collective, non-redundant predictability. Retention tracks persistence. None of the three tracks integration.

What it leaves to QUESTION-115

Whether boundary, timescale and macrostate can be found together, by a specified search with an Occam price, that recovers known boundaries in controlled models such as CASE-101. Where effective information parts from the others on one shared system is untested. That ΦID emergence is maximized by the microstate rests on NOTE-987’s reading of the paper’s Theorem 1, which concerns the PID quantities, not Ψ, and THEORY-764 does not cover it.

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