Time · Illumina — The Living Derivative

Abstract — The Pulse of Becoming

We present a minimal geometry in which “time” arises as a derivative density of energy distribution. Treating time as fundamental (realist stance), we posit that lawful structure may itself evolve; the rate of evolution couples to curvature in the temporal density. We supply a dimensional skeleton, a canvas simulation of an E(x,y) field, and a 160 Hz perceptual sonification of temporal curvature.

Unified Temporal–Energetic Geometry (UTEG)

Hypothesis

τ   :=  E / c³
∇τ  :=  ( ∇E ) / c³
τ̈   ⇄  ( ∇²E ) / c³

Dimensional Analysis

[E]=kg·m²·s⁻²; [c³]=m³·s⁻³ ⇒ E/c³ ~ kg/m. This is a density-like quantity, not a clock. Gradients and curvature of τ bend histories. Interpreting τ̈ as perceptual “tightening/loosening” motivates the 160 Hz sonification.

Derivation Notes (Sketch)

Given an energy texture E(x), define τ(x)=E(x)/c³.
Local coherence (phase) depends on ∂τ/∂x; instabilities scale with ∇²E.
If “laws evolve”, write L̇ ∝ f(τ, ∇τ, τ̈). Take f ≈ α·τ̈ (α>0).
Observable: frequency drift ∝ τ̈; attention wells at ∇²E peaks.

Discussion — Cultural Harmonics

Choruses, electoral cycles, rumor waves act as macroscopic interference patterns in τ. Peaks in ∇²E align with compressed rhythm (accelerated perception). The instrument below renders hue≈arg(∇E), saturation≈|∇E|, brightness≈∇²E; the τ̈ slider brightens curvature and modulates a 160 Hz tone.

Appendix — Core Equations of the Time Field

τ       =   E / c³
∇τ      =   ( ∇E ) / c³
τ̈      =   ( ∇²E ) / c³
Δτ/Δx   =   ( ΔE / Δx ) / c³
E       =   hν  =  mc²
t   ~   m / c