Introduction. Emergence is usually asserted. Information theory now offers ways to measure one version of it. Partial information decomposition (PID), introduced by Williams and Randall Beer in 2010, splits the information several sources carry about a target into unique, redundant and synergistic parts; synergy is information available only from sources taken jointly. Rosas and colleagues built on this to define causal emergence in multivariate dynamical systems: a macroscopic variable is causally emergent if it carries information about the system’s future that no microscopic element carries on its own. They distinguish downward causation (the macro variable predicts individual micro elements) from causal decoupling (the macro variable predicts only itself and other macro features), give practical criteria computable from ordinary mutual information that scale linearly with system size, extend the framework to observational data in the Granger sense, and publish code. A separate line, Hoel’s causal emergence, measures whether a coarse-grained description has more effective information than the fine-grained one. The caveats are real: PID has several non-equivalent definitions of redundancy, the measures are young and contested, and the choice of macro variable and coarse-graining is a researcher degree of freedom.
Important authors. Fernando Rosas (Imperial College London, now University of Sussex) and Pedro Mediano (Imperial College London) lead the information-decomposition approach to emergence, with Anil Seth (Sussex), Adam Barrett and Daniel Bor. Erik Hoel developed the effective-information account with Giulio Tononi. Paul Williams and Randall Beer at Indiana University introduced PID. Joseph Lizier (Sydney), Michael Wibral (Göttingen) and Nils Bertschinger and Jürgen Jost (Max Planck Institute for Mathematics in the Sciences, Leipzig) are the principal contributors to the PID definitional debate.
Importance for cybernetics and the VSM. Beer’s teaching that the five systems are “identifiable but not separable”, and the claim that the S1–S2–S3 assembly has properties its components lack, are emergence claims. Until recently they could only be argued. They can now be computed on time series an organisation already keeps—ticket flows, scheduling data, escalation logs—without intervention. Cybernetics has had “the whole is more than the sum” as a slogan since Ashby and Wiener; this is the first instrument that gives the slogan a null hypothesis. The VSM community has not used it.
Importance for the article. Demonstration IV, claim IVd (§9.1–9.4), states the emergence claim for the S1–S2–S3 assembly and applies the Rosas framework to the organisational time series collected for IIIc; §4.4 requires the macro variable and estimator to be named in advance; §10.5 places it at stage four; §12.7 makes it one of the instruments for the decomposability bet, and §9.4 says what is reclassified if the assembly is not emergent (subgraph claims become shorthand for node claims) and what is gained if it is (first quantitative support for “identifiable but not separable”). The import is from Variety and Channels Now §6 (C4), which also supplied the caveats. A reviewer will press on the PID non-uniqueness, on whether the emergence criteria have been validated on systems as small and noisy as an organisational log, on macro-variable preregistration as the many-analysts problem in another form, and on the distinction between Rosas-style and Hoel-style emergence, which are not the same quantity.
Sources in the reading list.
- the definitions of downward causation and causal decoupling, the practical criteria, and the observational-data extension IVd relies on.
Other important sources and authors.
- Williams, P. L., & Beer, R. D. (2010). Nonnegative decomposition of multivariate information. arXiv:1004.2515 — the original PID; note the co-author is Randall Beer, not Stafford Beer.
- Mediano, P. A. M., Rosas, F. E., Luppi, A. I., Jensen, H. J., Seth, A. K., Barrett, A. B., Carhart-Harris, R. L., & Bor, D. (2022). Greater than the parts: a review of the information decomposition approach to causal emergence. Philosophical Transactions of the Royal Society A, 380(2227), 20210246 — the authors’ own review, including the caveats and later refinements.
- Hoel, E. P., Albantakis, L., & Tononi, G. (2013). Quantifying causal emergence shows that macro can beat micro. Proceedings of the National Academy of Sciences, 110(49), 19790–19795 — the effective-information account; the rival definition a reviewer may expect to see distinguished.
- Bertschinger, N., Rauh, J., Olbrich, E., Jost, J., & Ay, N. (2014). Quantifying unique information. Entropy, 16(4), 2161–2183 — one of the competing PID definitions; the source of the non-uniqueness caveat.
- Lizier, J. T., Bertschinger, N., Jost, J., & Wibral, M. (2018). Information decomposition of target effects from multi-source interactions: perspectives on previous, current and future work. Entropy, 20(4), 307 — the editorial survey of the PID debate.
- Seth, A. K. (2010). Measuring autonomy and emergence via Granger causality. Artificial Life, 16(2), 179–196 — the Granger-based precursor; also a measure of autonomy relevant to §2.1’s fifth sense of viability.