How could one grain of wheat, doubled across a chessboard, outgrow the world?

Because doubling grows faster than anyone expects. Put one grain of wheat on the first square of a chessboard, two on the second, four on the third, and keep doubling. By the end, the board holds 18,446,744,073,709,551,615 grains, about 1,199 billion tonnes of wheat: more than 1,400 times what the whole world grows in a year.

The legend goes like this. The inventor of chess asks his ruler for this modest-sounding reward. The ruler laughs at such a meager prize, until his treasurers report that the grain would outstrip everything he owns. In some versions the inventor becomes a high-ranking advisor; in others, he is executed.

The trick is that each square holds as much as all the previous squares combined, plus one. The first half of the board adds up to about 279 tonnes, a big pile but a manageable one. Then the second half explodes: the 64th square alone holds more than two billion times the entire first half.

Our brains are bad at this. Studies show it, and there's even a name for it, exponential growth bias. We systematically underestimate anything that compounds, from savings to the early spread of a virus.