Exponential intuition
Humans think in straight lines, which is why exponentials keep ambushing us, in pandemics, compound interest, and AI. Fold a single sheet of paper in half enough times and it would reach the Moon. Move the slider and watch a thickness you can't see cross the solar system.
Thickness after folding
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The chessboard, too
Put 1 grain of rice on square 1, double it each square. By a given square you have:
Why this matters now
The first half of the chessboard looks manageable; the second half is astronomical, and that is exactly where many people misjudge technology curves, including AI capability and cost. The same math, in gentler form, is the engine behind the 1% compounding effect on habits, and the unsettling version drives Twelve Doors. Once you feel exponentials in your gut, a lot of the future stops looking surprising.