Thomas F. Varley, Erik Hoel (2022), Philosophical Transactions of the Royal Society A (vol. 380, issue 2227, art. 20210150; theme issue “Emergent phenomena in complex physical and socio-technical systems”) — ARXIV-2104.13368
Key takeaways
- Coarse-graining can convert redundant information into synergistic information, not merely discard information. In Boolean networks built so that past-to-future mutual information is identical at micro- and macroscale, the macroscale’s PID “synergy bias” still rises.
Seeded from the abstract and a skim, before the reading in NOTE-020. What follows is what the work says about itself.
The authors ask whether reduction is always a good scientific strategy, noting that special sciences above physics exist. Earlier work showed that macroscales can raise dependency between system elements (“causal emergence”). The paper proposes an umbrella framework in which emergence is the conversion of information from one type to another under a change of scale. Applying PID to the mutual information of Boolean networks, and introducing a “synergy bias” measure, they show that synergy can grow at the macroscale even when total mutual information is unchanged. They argue that universal reduction would therefore generally lose synergistic information.
Standing in the record
Filed by the reading-time triage of 2026-09-25: 1,255 seconds of active reading over 4 sessions in the papers-feed tracker. It was filed Deferred, unread. NOTE-020 is the close reading of 2026-09-25, and it placed the work: Active — a clear, small-scale demonstration that coarse-graining can change the redundant/synergistic composition of information and not just its amount. It is worth reading as the explicit cross-scale counterpoint to the ΦID account (item 21). Its “unifying theory” is a framing: the EI section re-describes a known decomposition and contains no new result.
When seeded, before the reading in NOTE-020, the entry gave a priority for a deeper reading: medium — A conceptually interesting counterpoint to item 21 (t = 1255 s already spent). The skim captures the argument, and further value comes mainly from comparing it with the ΦID account.
What the seeding asked a deeper reading to check (NOTE-020 is that reading):
- The “proof” of conversion depends on the equivalence-class construction. Check whether the effect survives for coarse-grainings found in real data rather than built by expansion, and how robust it is to the choice of redundancy measure (PID is not unique).
- It is in direct conversation with item 21. A deeper read should set the two definitions of emergence side by side.
- ML link, stated honestly: the Discussion mentions choosing the level of abstraction for comparing deep networks (citing Cao & Yamins) as one application. The paper itself has no ML experiments.
Access when seeded: Crossref metadata and abstract for the DOI (online 2022-05-23). Royal Society PDFs were blocked (403). I read the full text of the arXiv preprint 2104.13368v1 (27 Apr 2021, 20 pp.): figure captions for Figs. 1–4, §3.2 and the Discussion including §5.1. The keywords above are mine.