Compounding

Our brains evolved to think linearly. Add a little, get a little more. But when something grows by a percentage — multiplying rather than adding — the results quickly exceed anything our intuition can grasp.

Puzzle 1: The Lily Pad

A lily pad in a pond doubles in size every day. On day 30, it completely covers the pond. On what day did it cover half the pond?

Day 1 — 0.0000001% covered

Puzzle 2: The Penny

Would you rather have $1,000,000 today, or 1 penny that doubles every day for 30 days?

Day 1

$1 Million

$1,000,000

Doubling Penny

$0.01

Watch Them Diverge

Linear growth adds a fixed amount each period. Exponential growth multiplies by a fixed percentage. Start them equal and watch what happens.

Linear Start: 100

Linear: +10/period

Exponential Start: 100

Exponential: +10%/period

Periods: 30

Linear Growth

Exponential Growth

Linear Final

400

Exponential Final

1,745

Difference

4.4x

Why This Matters

Compounding isn't just about money. It's a fundamental principle that appears everywhere:

Knowledge: Each discovery enables the next. Science accelerates because we build on what came before.
Technology: Moore's Law — computing power doubling roughly every two years — has held for decades. Small percentages, staggering results.
AI Progress: Ray Kurzweil's "Law of Accelerating Returns" suggests technological change itself is exponential. This is why AI timelines are so hard to predict — our linear intuition fails us.
Habits: Small improvements (1% better each day) compound into transformative change. Small degradations compound into decay.

The lesson: when something grows by multiplication rather than addition, trust the math, not your intuition.