Vincent Vi

Tinkering · experiment 005

Step by step, ferociously

An explorable note on compounding, after Bret Victor's reactive documents. The green numbers aren't illustrations — they're the model. Drag them.


Say you get 1.0% better at something every day, and you keep it up for 365 days. The effort simply added up would make you 4.7× better. But each day's gain stands on all the days before it, so you actually end up 37.8× better.

drag the green numbers ↔ · or focus them and use arrow keys

Two readings of the same two numbers — the curve, and the letterform.

one letter, three sizes

↑ past the top of the frame

growth multiple over time — hover to read exact values

day 1 ×1linear ×4.7compounding ×37.8

The same lowercase a on one baseline: where you start, what the effort adds up to, and what it compounds to.

View as table
DayCompoundingLinear

1.01365 ≈ 37.8

a year of tiny gains

0.99365 ≈ 0.03

a year of tiny slips

That asymmetry is the whole argument for gradatim ferociter: the size of the step matters far less than refusing to skip one. Notice what the chart does when you drag the rate down to 0.3% — the curve doesn't flatten into the linear line, it just takes longer to leave it.