The Quiet Derivative

Another temporary writing, placed here to establish the shape of the section. The premise is simple: local behavior can be revealing without pretending to explain the entire system.

For a scalar field $g$, the local change in a direction $v$ is

$$ D_v g(x) = \nabla g(x)^\mathsf{T}v. $$

import numpy as np

def directional_change(gradient, direction):
    return float(np.dot(gradient, direction))

This entry is intentionally placeholder prose. It can grow into a technical essay, a short research note, or a notebook-backed explanation.