Source
Tissot, Levin, Buckley & Watson (2024), LIT-989, bioRxiv 10.1101/2024.02.16.580248, read in full in NOTE-773 (v2 of 2024-05-17, compared with v1): Model, Experiments and results (Figs. 4–9), Discussion, Appendix A.
What was actually shown
A simulation. Units are bistable deciders whose decision cycle γ_i(t) = (sin(ωt + θ_i) + 1)/2 alternates between a sensitive, inactive phase and an acting, insensitive one. They play a coordination game with couplings c_ij = 1 inside modules of ten and 0.01 across (Eq. 1), thirty modules in all. Each unit adjusts only its phase: θ_i ← θ_i + ν Σ_j (π/4) c_ij sgn(s_i s_j) sin(θ_j − θ_i) (Eq. 5), so it moves toward partners it currently agrees with and away from those it does not.
- Without the phase rule, 0 of 50 runs reach a global optimum; each module settles and “always re-make[s] the same decision”.
- With it, phases synchronise within modules, the modules “wake up” suddenly (most before t = 20,000), and with the learned phases 50 of 50 runs from random states reach a global optimum. Blocks of ten switch together, “acting like a single macro-scale unit”.
- Control. Synchrony imposed on all 300 units produces no transition and no gain (Fig. 7A).
- Mechanism, as the authors give it. When a module’s members are sensitive at once, none is acting on the others, so the weak external pull is the only one left: attention turns “from the ingroup to the outgroup”. No signal passes inside the module; the authors stress it has “no internal computation or information integration”.
- Selection does it too (Fig. 8), in a 7 × 7 version, about a hundred times more slowly.
What could have come out the other way: synchrony could have spread globally, or formed within modules and changed nothing, as global synchrony does. The phases moved toward within-module synchrony before any collective benefit was available (Fig. 5B).
What this does not say
- That timing draws the boundary. The modules are built into c_ij; the authors say they “clearly prescribe the boundaries of the collectives”. Timing finds and enacts a boundary the couplings already have.
- That entrainment as in coupled oscillators does this. The phase rule is a gradient on cycle-averaged payoff, “loosely analogous” to Kuramoto entrainment, and Appendix A derives it under an approximation. No run uses coupling through the units’ outputs.
- That the module is an agent beyond the minimal sense. It chooses between two collective states so as to lower collective stress, and nothing more: no boundary in space, no metabolism, no integration.
- That it generalises. One game, clean and consistent modules, one parameter setting, no sweep; the authors expect natural interactions to be graded and frustrated.
- That the higher level does anything the micro level does not. “The higher-level agent is not a variable in any of our equations of motion.” The claim is that the organisation of timing changes outcomes, not that a macro variable acts.
Connections
- QUESTION-035. A worked case for the first and second clauses
relative to a stated target (resolving the between-module
constraints): the unit is the synchronised module, and membership is
“who is synchronised with whom”. On the third clause it shows formation
and persistence of the learned phases across changed games, not
dissolution. No
answers:is declared: it is a case an answer must handle, built with the boundary given. - CLAIM-172. Corroborates it in the within-module case and sharpens it: relative to this target, common timing as such made no unit (the global control); timing matched to the strong couplings did. CLAIM-172’s defeat condition, which any complete micro simulation like this one met as first written, was reworded on 2026-10-14 to ask for descriptive economy (its version 6).
- CLAIM-157. The couplings are nearly decomposable from the start, so the block criterion returns the same verdict before and after the transition, while the module’s behaviour as a unit changes. One system by coupling and a responding unit by timing come apart here.
- THEORY-232. The model Watson’s essay cites as unpublished. Fig. 6 computes in effect THEORY-232’s comparison of equilibrium energy under the old and new organisation, with the decomposition and goals stipulated, as THEORY-232 says they must be.
- THEORY-069. HKB entrainment is through the effectors’ coupled dynamics; this is through a payoff rule on phase. They share the word and the sine term, not the mechanism.
Note of 2026-10-29: re-run by the status review
The sixteenth status review re-implemented the model from NOTE-773’s equations (v2 Eqs. 3–5: N = 300, k = 10, c_ij = 1 within and 0.01 across, c_ii = 0, I(x) = clip(100x, ±1), noise uniform ±0.01, ω = 0.01, ν = 3·10⁻⁵). It learned phases for 30,000 steps, then ran 50 tests of 20,000 steps from random states with the phases frozen. A run counted as a global optimum if every unit’s sign, averaged over the last cycle, was the same.
- Learned phases: within-module phase coherence 0.97–0.99; 50, 50 and 26 of 50 runs at the optimum for three learning seeds, and 50 of 50 for the third after 60,000 learning steps. Every module flip went toward the other modules’ majority.
- Random phases: 0 of 50 for every seed.
- Learned phases shuffled across units (the same phases, with the match to modules destroyed): 0 of 50.
- Synchrony matched to modules, imposed by hand: 50 of 50. Module-matched synchrony is what does it.
- Global synchrony: 8–19 of 50 runs ended at an optimum, but not by modules responding to one another. About 15 of 30 modules flipped each cycle, 16% of flips went toward the others’ majority, and in 46% of cycles more than half the modules flipped at once: the whole system resets each cycle and an all-agree state appears transiently. The paper’s Fig. 7A is reproduced for modules responding as units, not for the end state.
- Self-coupling c_ii = 1: the same pattern.
- Beyond the paper’s setting: with within-module couplings graded (uniform 0.2–1.8), the result holds at across-coupling 0.01. At 0.03, random phases already reach the optimum in about half the runs, and at 0.1 or more in all of them, so there is no lock-in for timing to undo. The slowest phase rate tried, 10⁻⁵, did not synchronise modules within 30,000 steps. Overlapping modules, frustrated constraints and entrainment through the units’ outputs were not run; they are QUESTION-337.
The re-run is the record’s own, from a transcription whose figures were read from their captions only.