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 better. But each day's gain stands on all the days before it, so you actually end up 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
| Day | Compounding | Linear |
|---|
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.