Yes, woo — on purpose. The name is a filter: if it makes you dismiss this, it isn’t for you. The work is to interpret the dynamics, not to fixate on the numbers (the numbers are rigorous anyway — see Methods). A latent dynamical system: each actor is a vector z∈ℝ10 descending a continuous potential1 on a directed, plastic graph.9
click node = lock (role-lock) · drag node = move in-plane (basin test) · drag timeline = scrub · space pause · R reset
Computational instrument — interactive specification, v0.4 “the Third.” · We call it “woo” deliberately: the name selects for readers who interpret dynamics over those who fixate on data. The mathematics below is, nonetheless, exact.
Each of N actors carries a latent state zi(t)∈ℝ10 over interpretable affective–relational coordinates [security, threat, desire, status, intimacy, ambiguity, control, shame, curiosity, trust], a circumplex-style decomposition of interpersonal affect.14 The display is a 2-D coordinate projection pi=Π(zi); the field is the corresponding planar slice of the full potential.
States evolve by gradient descent on a continuous potential, plus directed coupling, perturbation, and stochastic forcing — a Langevin flow on an attractor landscape in the tradition of associative-memory1 and continuous neural-field models,2 over a Waddington-style landscape metaphor.3
Attractor strengths Ak(t) = Ak(1 + b·sin(ωkt + φk)) “breathe,” a slow periodic modulation analogous to coupled-oscillator entrainment.8 Coupling strength κ is the order parameter of an interaction phase transition: above a critical κ the constellation collapses into a single basin — a saddle-node/catastrophe-type bifurcation.456 Coordination-dynamics models of dyadic coupling motivate the directed term.7
The directed graph is not fixed. Weights relax toward a structural prior W₀ and are driven by a lagged, motion-gated directional alignment — a Hebbian9 proxy for directed causal influence in the spirit of Granger causality10 and transfer entropy.11 If i’s motion at t−1 predicts j’s motion at t, Wij grows.
U = ΣiU(zi) is the system potential energy. The Kuramoto-style order parameter R = ‖N⁻¹Σi vi/‖vi‖‖∈[0,1] measures directional coherence of motion (R→1 at collapse).8 Coupling asymmetry Δ = ⟨|Wij−Wji|⟩ quantifies net directedness. Basin occupancy assigns each actor to argmink‖zi−ck‖.
Perturbation is treated as measurement: a controlled input Pi(t) deforms the landscape and the response reveals coupling — an active-inference reading of probing.15 The framework follows the dynamical-systems program for social and dyadic psychology.1213
A two-body system — a dyad, or a single actor in a fixed landscape — is effectively integrable: it settles. Sociologically, Simmel argued the triad is categorically distinct from the dyad; the third party transforms every relation it enters (mediator, tertius gaudens, divide-and-rule).16 Dynamically, the analogue is exact: adding a third gravitating body destroys integrability and admits chaos — Poincaré’s three-body problem18 and its sensitive dependence on initial conditions, quantified by a positive largest Lyapunov exponent.19 We add a third body with mutual coupling to the actor cloud and measure λ online with the Benettin twin-trajectory method. With the Third off, λ ≈ 0 (the dyad settles); switch it on and λ > 0 — the system becomes perpetually generative.
The Third has two archetypes along an axis μ∈[−1,+1]:
Moloch (μ > 0): the coordination-failure attractor. Its pull scales with the group’s own coherence — the more the actors harmonize, the harder it drags them toward the “sacrifice” well, inflaming competition. This is the multipolar trap: the tragedy of the commons,20 Schelling’s perverse macro-behaviour,21 the god to whom cooperation is sacrificed.27 Girard’s mimetic third — the model-rival who generates desire and rivalry — is the interpersonal face of the same force.17
The hidden Buddha (μ < 0): the empty witness. It applies a rotational, de-grasping force — weakening attractor capture and inducing orbit rather than collapse. It is “hidden” (low amplitude, never dominating) yet decisive: by refusing to fix the system it keeps it in continual becoming — the non-substantial third of Nāgārjuna’s śūnyatā and dependent origination.24
Either way the moral is one: adversity is the engine of complexity. A frustrated system explores; order arises through fluctuation far from equilibrium (Prigogine’s dissipative structures22) and richness peaks at the edge of chaos.23 The dialectic needs its negation: the third moment that sublates the pair into a higher unity.25 We report this as complexity C, the rate of basin reorganization. The directed graph is the Symbolic order through which the Third becomes legible.26
| object | contemplative reading | formal object |
|---|---|---|
| attractor well | a samskara / habitual refuge | local minimum of U(z) |
| perturbation | a koan, a rupture, grace | impulse input P(t); a measurement |
| breathing | the field inhaling/exhaling | periodic modulation Aₖ(t) |
| Moloch | the demon of sacrificed cooperation | coherence-coupled adversarial attractor |
| hidden Buddha | śūnyatā, the witness, non-grasping | rotational, attractor-attenuating operator |
| λ > 0 | irreducible aliveness / freedom | positive Lyapunov exponent (chaos) |
| complexity C | growth through adversity | basin-transition rate (order-through-fluctuation) |