shapes

The nouns change — loss, calibration error, portfolio risk — but the procedure is one: pick a number to improve, move through choices, stop when improvement runs out. Once you read it once, you recognise it everywhere.

Two opposing forces, one point where they cancel. The shape underneath the pendulum, the falling raindrop, and the optimal portfolio: name the forces, write the balance equation, solve for where the net change vanishes.

The forward model is easy: given inputs, compute the output. The inverse is the question that actually matters: given the output, recover the input. Most of finance and most of model calibration is the inverse direction of an equation that's trivial forward.

High-dimensional data with too much redundancy. Change basis until most coordinates are small. Drop the small ones. Reconstruct what's left. JPEG, TF-IDF, and Huffman codes are the *same procedure*, just applied to pixels, words, and probabilities.