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The Physics of the Dancing \emph{Deity}: Coupled Oscillators in Himalayan Processions

Nalin Dhiman

TL;DR

The paper models Himalayan procession raths as coupled oscillators: a six-DOF rigid body with unilateral contact interacts with human carriers whose gaits form Kuramoto-type phase ensembles, while musical entrainment and guru semantics act as global and semantic couplings. It shows that near-perfect synchronization can coincide with large-amplitude rocking and episodic unloading due to nonlinear unilateral contact, a finding supported by Archival Palanquin Simulator runs that reveal distinct baseline and music regimes. The approach demonstrates explanatory pluralism, linking a mechanistic dynamical system with phenomenology and ethics, and yields falsifiable predictions about beat-locking, vertical motion, and harmonic content that can be tested with noninvasive measurements in field settings. The work emphasizes that agency in procession motion is distributed across physics and social meaning, rather than residing in any single actor, and provides a framework for studying how ritual couplings stabilize collective interpretation.

Abstract

In parts of Himachal Pradesh (Kullu and Mandi) and the Western Himalaya, village deities (\emph{devtā}) are carried through the landscape on shoulder-borne palanquins or ``raths.'' Participants often describe these raths as agents: they \emph{choose} routes, signal assent or refusal, and sometimes ``move on their own'' as if people are not moving them but are instead being moved. This paper offers : (i) a mechanistic model in which a palanquin interacts with human carriers modeled as coupled limit-cycle oscillators, and (ii) a philosophical analysis of how music and gurus/oracular specialists (\emph{gūr}/``guru'' in local English) function as couplings that stabilize collective interpretation, producing what we call \emph{distributed agency}. On the physics side we build a six-degree-of-freedom rigid-body model with unilateral handle contacts, base excitation from walking, and a Kuramoto-Adler phase description for interpersonal coupling and musical entrainment. We prove standard phase-locking conditions (Adler-type capture range) and show how unilateral contact can rectify periodic forcing and inject harmonics, creating parameter regimes in which near-perfect synchrony produces large-amplitude roll. On the simulation side we report an ensemble study (30 seeds per condition) from an archived ``Palanquin Simulator'' package: a ``baseline'' condition produces small roll (\(\mathrm{RMS}\approx 0.15^{\circ}\)) and moderate synchrony, whereas a ``music'' entrainment condition produces near-unity synchrony (\(\approx 0.99\)) but also robust roll instability (\(\mathrm{RMS}\approx 18^{\circ}\)) and frequent contact loss. We do \emph{not} claim to have validated the model against field data; we treat the simulations as a \emph{proof of plausibility} and as a generator of falsifiable predictions.

The Physics of the Dancing \emph{Deity}: Coupled Oscillators in Himalayan Processions

TL;DR

The paper models Himalayan procession raths as coupled oscillators: a six-DOF rigid body with unilateral contact interacts with human carriers whose gaits form Kuramoto-type phase ensembles, while musical entrainment and guru semantics act as global and semantic couplings. It shows that near-perfect synchronization can coincide with large-amplitude rocking and episodic unloading due to nonlinear unilateral contact, a finding supported by Archival Palanquin Simulator runs that reveal distinct baseline and music regimes. The approach demonstrates explanatory pluralism, linking a mechanistic dynamical system with phenomenology and ethics, and yields falsifiable predictions about beat-locking, vertical motion, and harmonic content that can be tested with noninvasive measurements in field settings. The work emphasizes that agency in procession motion is distributed across physics and social meaning, rather than residing in any single actor, and provides a framework for studying how ritual couplings stabilize collective interpretation.

Abstract

In parts of Himachal Pradesh (Kullu and Mandi) and the Western Himalaya, village deities (\emph{devtā}) are carried through the landscape on shoulder-borne palanquins or ``raths.'' Participants often describe these raths as agents: they \emph{choose} routes, signal assent or refusal, and sometimes ``move on their own'' as if people are not moving them but are instead being moved. This paper offers : (i) a mechanistic model in which a palanquin interacts with human carriers modeled as coupled limit-cycle oscillators, and (ii) a philosophical analysis of how music and gurus/oracular specialists (\emph{gūr}/``guru'' in local English) function as couplings that stabilize collective interpretation, producing what we call \emph{distributed agency}. On the physics side we build a six-degree-of-freedom rigid-body model with unilateral handle contacts, base excitation from walking, and a Kuramoto-Adler phase description for interpersonal coupling and musical entrainment. We prove standard phase-locking conditions (Adler-type capture range) and show how unilateral contact can rectify periodic forcing and inject harmonics, creating parameter regimes in which near-perfect synchrony produces large-amplitude roll. On the simulation side we report an ensemble study (30 seeds per condition) from an archived ``Palanquin Simulator'' package: a ``baseline'' condition produces small roll () and moderate synchrony, whereas a ``music'' entrainment condition produces near-unity synchrony () but also robust roll instability () and frequent contact loss. We do \emph{not} claim to have validated the model against field data; we treat the simulations as a \emph{proof of plausibility} and as a generator of falsifiable predictions.
Paper Structure (37 sections, 1 theorem, 25 equations, 4 figures, 1 table)

This paper contains 37 sections, 1 theorem, 25 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction: a rath that "moves"
  2. Explanatory pluralism and the scientific/social boundary
  3. A minimal mechanical model
  4. Rigid-body state on $\mathbb{R}^3\times \mathrm{SO}(3)$
  5. Handle geometry and contact kinematics
  6. Unilateral viscoelastic contact
  7. Newton Euler equations
  8. Carriers as coupled oscillators
  9. Why phase models?
  10. Kuramoto-type interpersonal coupling
  11. Musical entrainment as injection locking
  12. From phase to forces: base excitation
  13. Why nonlinearity matters: rectification and harmonics
  14. Conditions for rocking: a dynamical-systems view
  15. A forced-oscillator caricature
  16. ...and 22 more sections

Key Result

Theorem 1

Consider eq:adler with constant $\Delta\omega_m$ and $K_m>0$. If $\left\lvert \Delta\omega_m \right\rvert<K_m$, there exists a stable fixed point $\Phi^\star\in(-\pi/2,\pi/2)$ satisfying $\sin\Phi^\star=\Delta\omega_m/K_m$. If $\left\lvert \Delta\omega_m \right\rvert>K_m$, no fixed point exists and

Figures (4)

  • Figure 1: Ensemble distributions for the three key observables. Music entrainment produces a near-deterministic shift toward high synchrony, large roll amplitudes, and sustained contact loss in this archived parameter regime.
  • Figure 2: Representative roll angle trajectories from the archived simulator logs.
  • Figure 3: Kuramoto order parameter $r(t)$ for representative baseline and music runs. Music entrainment produces near-unity synchrony.
  • Figure 4: Representative simulation frames comparing baseline vs music entrainment. The top row shows baseline dynamics (no beat-driven phase entrainment), where the palanquin remains comparatively level under the same rigid-body + unilateral-contact model. The bottom row shows runs with music/drum entrainment enabled, where stronger phase locking among carriers produces a visibly more tilted/rocking palanquin configuration (roll/pitch amplification). All panels use the same visualization convention: the rigid body (blue box), poles/handles (black), and carrier/handle contact markers (red).

Theorems & Definitions (2)

  • Theorem 1: Phase locking for musical entrainment
  • proof