Source
Varley & Hoel (2022), LIT-027, “Emergence as the conversion of information: a unifying theory”, read in full in NOTE-020.
What was actually shown
The measure (Eq. 8). A partial information decomposition of I(X; Y), sources the past states of the elements and target the joint future (Eq. 7), with the Williams–Beer I_min redundancy (Eq. 6). Grouping the atoms by lattice height gives a spectrum S_i, and the synergy bias is B_syn = Σ (i/|S|)·S_i, normalised so systems of different sizes compare.
Logic gates (Table 1). An XOR built from NAND, AND and OR has B_syn 0.52 as a micro network and 0.833 as a macro gate. But mutual information also falls, from 2.5 to 1 bit, so these cases mix a change of type with a loss. The authors say so.
The expansion method (§3.2). Split one node of a 3-node macroscale into an equivalence class of children with the same inputs and outputs, giving 4- and 5-node microscales. Mutual information is unchanged and inconsistency is zero by construction.
- In all 200 positive-Gaussian systems, B_syn is higher at the macroscale. The gain, read off Fig. 4, is about 0.005–0.07 on a scale from 0 to 1, and correlates with macroscale B_syn at r = 0.819.
- In the 185 near-deterministic systems, those with macroscale B_syn below about 0.5 mostly lose synergy bias at the macroscale, down to about −0.1.
What could have come out otherwise. With mutual information and consistency held fixed, B_syn could have been identical across scales. It was not, in either direction.
What this does not say
- That macroscales convert redundancy into synergy. That held for one generated class. For deterministic, redundancy-biased systems it mostly ran the other way. The abstract and title do not say so.
- That the result holds for another redundancy measure. Only I_min was used. The authors note that it is criticised and that PID redundancy has no gold standard. The critiques are now held: I_min credits independent sources copied into the target with a full bit of redundancy, and so overstates synergy by the same amount where sources are copied (THEORY-708, THEORY-705). Whether that touches these Gaussian systems was not recomputed.
- That the conversion is a property of the system rather than of the construction. Equivalence-class children share inputs and outputs. If they behave as copies, part of the microscale’s extra redundancy is put there by the expansion. NOTE-020 could not check the splitting rule without the supplementary code.
- That it is a unifying theory of emergence. The EI section restates EI = determinism − degeneracy and re-describes causal emergence as converting transition uncertainty into EI, with no new result. Nothing is shown for integrated information or any other measure.
- That any real system does this. The macroscales have 3 nodes and the data are generated TPMs.
Connections
- Effective-information emergence (THEORY-222) is Hoel’s earlier account, which this paper folds under “conversion” by re-description. It adds no evidence to that account.
- The ΦID account (THEORY-497) places emergence in one description’s synergy about its own future, not in a change across descriptions. Its review cites this paper for the claim that ΦID lacks a macro–micro comparison and calls that a misunderstanding. On NOTE-020’s reading, splitting a node into equivalence-class children is, for ΦID, a change of partition, under which its atoms are expected to change and which it does not count as emergence.
- Local values (THEORY-268). Varley’s later paper shows the expected quantities used here can be positive while negative at particular transitions.
- The theme issue’s editorial (LIT-021) repeats the claim that this paper “overcomes the … dichotomy between strong and weak emergence”. NOTE-007 records that the body does not support it.