A Small Clockwork for Uncertain Things

Tue, 11 Aug 2026 00:00:00 +0000

This is a placeholder for a longer note. Suppose a small mechanism turns noisy observations into a useful signal, provided we resist the urge to make it sound more certain than it is.

The objective can be written in ordinary display math:

$$ \mathcal{L}(\theta) = \frac{1}{n}\sum_{i=1}^{n}\left(y_i - f_\theta(x_i)\right)^2 + \lambda \lVert\theta\rVert_2^2. $$

And a small executable thought can live alongside the prose:

def damped_update(value, gradient, step_size=0.1):
return value - step_size * gradient / (1.0 + abs(gradient))

The final version can replace this text with an argument, a result, or a question worth keeping open.

The Quiet Derivative

Tue, 04 Aug 2026 00:00:00 +0000

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.

Notes | Mahdi Kooshkbaghi

A Small Clockwork for Uncertain Things

The Quiet Derivative