Source
- Kelso (2021), “The Haken–Kelso–Bunz (HKB) model: from matter to movement to mind”, LIT-601, read in NOTE-467: §§2–4, Box 1 and the Appendix.
- Haken, Kelso and Bunz (1985), LIT-588, read in full in NOTE-1424: the model’s original statement, a theory paper with one simulation and no new data.
- Kelso, Scholz and Schöner (1986), LIT-1851, read in full in NOTE-1433: the first quantified report of critical fluctuations.
- Dynamic Patterns (LIT-578) is Unavailable; Schöner, Haken and Kelso (1986) and Scholz, Kelso and Schöner (1987) are not filed.
What was actually shown
The model, as Kelso states it. Kelso (LIT-601) takes the relative phase φ of the two index fingers as the order parameter. Its dynamics is dφ/dt = −a sin φ − 2b sin 2φ, with potential V(φ) = −a cos φ − b cos 2φ. Both φ = 0 (in-phase) and φ = π (anti-phase) are stable when b/a > 1/4, at slow movement. Below 1/4, at fast movement, anti-phase is unstable and only in-phase remains: a pitchfork bifurcation, with movement frequency as the control parameter. The φ equation is derived from two coupled nonlinear oscillators, one per limb (Eqs. 4–6), so the collective variable is obtained from the level below and not only fitted to it.
Hysteresis follows from the layout. Because both patterns are stable in the slow range, a system that has switched to in-phase at high frequency has no reason to return to anti-phase when the frequency is lowered again. Haken, Kelso and Bunz derive it so (LIT-588, p. 350) and report it as a feature of Kelso’s experiments, “(iv) when cycling frequency is reduced, the system stays in the symmetrical mode” (p. 348), but show no data, and no paper read here does.
The phase transition and its warning signs, as reported. With noise (Eq. 3, Schöner et al. 1986), the switch is a nonequilibrium phase transition. Kelso reports that “the hallmark features of nonequilibrium phase transitions including a strong enhancement of fluctuations and critical slowing down—‘anticipatory signatures’ of upcoming pattern change” were observed, and that the stochastic model fitted means, variances, relaxation times and switching times with a single free parameter. He quotes Haken that such fluctuations are hard to understand on a motor-programme account, which “does not allow any fluctuations”. This is the result that could have come out otherwise: a stored programme switching on a cue predicts an abrupt change with no growth of variability before it. Kelso, Scholz and Schöner (LIT-1851) show the fluctuations first-hand: the standard deviation of relative phase rises as anti-phase nears the switch and peaks in the transition, in wrist (30 runs, four subjects) and finger movements (ten runs, one representative subject), with no rise and no switch when the movement starts in-phase (Figs. 1–4); no statistical test is reported. Critical slowing is predicted there, not measured. The one fit of the stochastic theory read first-hand, Kelso, Scholz and Schöner 1988 (LIT-1873, NOTE-1449), is of intended switching, with one added parameter set to the order of magnitude and mean times above those observed.
Brain, as reported. Transcranial stimulation over premotor and supplementary motor cortex switched anti-phase to in-phase and not the reverse, as the model’s stability asymmetry predicts, and activity in several motor regions scaled with the instability of anti-phase. Cited, not read.
What this does not say
- Not that the mind is HKB. Kelso’s later sections extend the dynamics to coordination between people, with machines, and to “mind”. The claim here is about rhythmic bimanual coordination. The breadth is reported, and the retrospective’s inference that coupling is “informational” is the author’s (C4 in NOTE-467).
- Not that the dynamical model settles the mechanism. Kelso’s claim that deriving HKB from neural populations puts the mechanism-versus-description objection “to bed” is asserted, not argued.
- Not a global minimum principle. The potential V(φ) is a property of a one-dimensional flow, which always has one. It is no evidence of the kind of variational principle Cross and Hohenberg (LIT-527) find absent in pattern formation away from equilibrium, except near threshold.
Connections
- The unity it is about.
behavioral-integration: Bernstein’s problem of many degrees of freedom acting as one, answered by a collective variable and not by a controller. The record’s other accounts of integration work by competition (THEORY-068), arbitration or bargaining; this is the dynamical alternative. It is not about a self or a subject (ADR-024). - Complex systems. Rizi (LIT-150) locates the onset of emergence by order parameters, diverging susceptibility and correlation length, and asserts that weak emergence is all science needs. HKB is a case in the record where an order parameter and a control parameter were identified in human behaviour and critical fluctuations reported. Cross and Hohenberg (LIT-527) describe patterns near onset by low-dimensional amplitude and phase equations; HKB’s reduction to one phase variable near an instability is that strategy applied to limbs.
- THEORY-058 (mental disorders as alternative stable states of
self-reinforcing loops). That account borrows hysteresis and critical
slowing from the physics of phase transitions, and the record notes it
does so without an order parameter or a measured transition. HKB is the
record’s case of the same signatures with both, in human behaviour, so it
shows the kind of evidence THEORY-058’s
promote_whenasks for can be obtained from people. It is no evidence that disorders behave this way, and no relation is declared. - THEORY-056 (control without a distinct regulator). HKB’s pattern changes are not chosen by any controller. It is a neighbour in architecture, about movement and not motive, and no relation is declared.
- Participatory sense-making (LIT-571) and Raja et al. (LIT-598) take Kelso’s coordination dynamics as given: the first for relative coordination between people, the second as a system already explained by its own collective variable, which a Markov-blanket partition does not improve on.
Note of 2026-10-30: what holds it back
Two of the promote_when’s findings are still not read first-hand: the growth of relaxation time before the switch, predicted in LIT-1851 and shown in Scholz, Kelso and Schöner 1987 (Physics Letters A 123:390), which is not filed; and hysteresis, which HKB 1985 reports from Kelso’s earlier experiments without data. The switch’s direction and the critical fluctuations are now read first-hand (LIT-1851). What CLAIM-172 needs of it, the model and the fluctuations, is split off as THEORY-1227, Active. A further split frees nothing: ARG-016 rests on CLAIM-169, Proposed.