Giulio Tononi, Olaf Sporns and Gerald M. Edelman (1994), Proceedings of the National Academy of Sciences 91(11), 5033–5037.
Key takeaways
From the reading, NOTE-767.
- The measure. Integration is I(X) = Σᵢ H(xᵢ) − H(X). Neural complexity is C_N(X) = Σ_{k=1}^{n} [(k/n) I(X) − ⟨I(X_j^k)⟩], which equals Σ_{k=1}^{n/2} ⟨MI(X_j^k; X − X_j^k)⟩. For Gaussian activity, I(X) = −ln|CORR(X)|/2.
- Both extremes are low. For Toeplitz covariance matrices (n = 64), C_N is very low at independence and at near-total correlation, and maximal when correlations span the range from 0 to 1. It is a worked example, not a proof.
- Patchy beats uniform. In a simulated visual area, the cortex-like patchy pattern gives C_N = 2244.7. The same connections spread uniformly give a higher I(X), global synchrony and C_N = 1240.2. In small linear systems, concentrating a fixed amount of connection on fewer partners raises C_N/I.
- Reciprocity and grouping. At constant I, C_N tends to rise with the number of reciprocal pairs. Dissolving neuronal groups lowers it, but that result is “data not shown”.
- Scope. The system is isolated, stationary and Gaussian, with homogeneous components fixed in advance. Validation on recorded brains is left to later work.
Standing in the record
Filed on 2026-10-12 for QUESTION-042, and read on 2026-10-14 in NOTE-767. It was registered as “the rival measure the Occam-priced block test must be compared with”. The reading shows it is not a rival of that kind. C_N scores a whole system and draws no boundary. It has no threshold and no Occam price, and its stationarity rules out short-lived blocks. Its point of contact with CLAIM-157 is its oneness condition: a system is an individual only if no bipartition has zero mutual information. That is the gap test with the threshold set to zero. THEORY-262 holds the measure’s two-extremes property and its link to patchy connectivity, at the strength the simulations give. No THEORY or CLAIM cited the paper before this reading.