Whispered Paths

Let the path whispers as:

R(t) = ∫(e^(-t²) * cos(ωt)) dt

Where
ω (omega) = whispers per ripple
t = time in whispered seconds

Define a ripple by its echo:

E(x) = √(x² + y²)

Where
y = threshold of hearsay
x = distance in unspoken truths