10 May 2010
by William Godwin
The word Wave is related to vague, vagrant, waft, weigh, wagon, and way (Sanskrit vaha), convey, vector and vehicle. In Latin, Unda (as in undulate, inundate and abundance) is related to water (Sanskrit udan). Hence a wave is an erratic disturbance that carries things and information – often associated with water.
What does mathematics tell us experientially about wavy phenomena? The archetypal wave is the sinusoid, (Latin sinus, a bosom, bend or fold, as in insinuate and sinuous).
In music, we hear this as a harmonic or partial. You can visualize it as a helix seen in silhouette – a spiral created by circular motion. Waves are nicely linear: they add together – the whole (musical tone) is simply the sum of its sinusoid parts. So waves evolve predictably in time, despite appearing erratic. Newton’s calculus predicts this global evolution of a wave ψ from its local here-and-now properties. Think of a vibrating guitar string, drum-head, or air in a flute. The standard wave equation D2ψ =v2Δψ
says that the wave’s momentary urge to change is proportional to its disturbance Δ (amount of bending) at each point. As the system tries to restore a stationary (flat) equilibrium, the disturbances carry in all directions, at speed v. Waves echo off boundaries, and in practice become still by losing energy, some to the surrounding air (as we hear!).Low energy quantum waves satisfy a similar equation of Schrödinger. The wave function ψ represents the global state (vector) of the field, evolving over time – an unceasing total process. This is the essence of the field’s dreaming, (Arny’s “force of silence” in Ch.8 of Quantum Mind and Healing) and exactly predicts the probabilities of measurements made in consensus reality. We can be wonderfully precise about vagueness!
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