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LIT-953: Flickering Emergences: The Question of Locality in Information-Theoretic Approaches to Emergence

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StatusActive — read 2026-10-14 (NOTE-756) in full; worth reading as the plain demonstration that information-theoretic emergence scores are expectations whose local values can run the other way: a coarse-graining emergent on average can turn most informative micro transitions into misinformative macro ones, and the ΦID synergy atom can be negative at particular transitions. Read it knowing that the instances are one constructed toy and one connectome, that the claim for every excess-entropy measure is argued and not proved, and that what a negative moment means is left open. Registered for QUESTION-035; THEORY-268 is filed from it.
Version2
Tagscomplex-systems, information-theory, individuation
Cited as “paper” byNOTE-756 — Varley — Flickering Emergences
Cited as “source” byTHEORY-268 — An emergence measure averaged over a system's transitions can be positive while its local value is negative at particular transitions, so emergence so measured belongs to the ensemble, not to each moment

Graph View

Thomas F. Varley (2022), Entropy 25(1), 54.

Key takeaways

From the reading, NOTE-756.

  • The identity underneath. Local mutual information i(x; y) = log P(x,y)/(P(x)P(y)) is negative whenever P(x,y) < P(x)P(y), while its expectation I(X; Y) is never negative. Local excess entropy e(x) = i(x_{t−1}; x_t) is negative when the past makes the realised future less likely than chance: “The past transiently ceases to inform of the future and instead misinforms.”
  • Coarse-graining. A four-node Boolean network, coarse-grained by AND over pairs, is emergent on Hoel’s measure (log(F̄(X̃)/F̄(X)) ≈ 0.202), yet ≈52.73% of informative micro transitions map to misinformative macro ones. They are the low-probability transitions, so the average holds.
  • ΦID synergy. The same toy’s macro system has temporal synergy ≈0.031 bit on average and a negative local value at 31.25% of its sixteen transitions.
  • A connectome. On one Human Connectome Project matrix with Infomap macro-nodes, ≈22.47% of informative micro edges map to misinformative macro edges, and ≈80.4% of misinformative edges run between communities.
  • How general. The possibility is argued to hold for any measure built on time-delayed mutual information; two further frameworks (Barnett and Seth, Chang et al.) are expected to show it, not computed.
  • What a negative moment means is open. It may be fluctuation or a change in causal structure; the statistics alone do not say.

Standing in the record

Filed on 2026-10-12 from the owner’s papers-feed for QUESTION-035, and read on 2026-10-14 in NOTE-756. The seed claim, that emergence can hold on average and fail at particular configurations, is confirmed. The reading adds that an average verdict on unity gives no verdict about a moment, which bears on the duration clause of CLAIM-157 and on the persistence test of CLAIM-161. THEORY-268 is filed from it: emergence measured as an expectation belongs to the ensemble of transitions, not to each moment. It complements THEORY-222, which holds the average effective-information gain of the same coarse-graining account.

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