Second Half of the Chessboard

Definition

Human intuition tracks linear change well but fails at sustained doubling. Using Ray Kurzweil's retelling of the chess-and-rice legend — one grain on square one, doubling each square, sixty-three doublings later — the book distinguishes the first half of the chessboard, where doubling numbers stay within the range of everyday experience (millions, billions), from the second half, where the same doubling process crosses into trillions and quintillions and "we lose all sense" of the quantities involved, even though nothing about the underlying process has changed.

In the Book

The chapter walks the legend through both halves: after thirty-two squares the emperor has given out about 4 billion grains, "a reasonable quantity...and the emperor did start to take notice," but crossing into the second half of the board is where the story turns fatal (in some versions the inventor is beheaded once the trick is understood). Brynjolfsson and McAfee then run their own version on Moore's Law: taking 1958 (when the U.S. Bureau of Economic Analysis first tracked "information technology" as a corporate investment category) as a starting point and eighteen months as a doubling period, thirty-two doublings put American business computing into the second half of the chessboard around 2006 — which the book uses to explain why science-fiction-grade technologies (self-driving cars, Watson beating Jeopardy! champions, cheap flexible robots) all arrived in a narrow recent window rather than gradually. It contrasts this with the steam engine, which also improved exponentially after Watt but through only three or four doublings over two centuries — slow enough that a "second half" was never reached.

Why It Matters

The concept gives a name to a specific failure of intuition: mistaking "progress has been modest so far" for "progress will continue to be modest," when the underlying process is exponential rather than linear. It applies anywhere a quantity compounds at a roughly fixed rate — compute, data, infectious spread, compound interest, viral reach — and explains why forecasters repeatedly get blindsided by the same shape of curve: they correctly observe the slow first half and wrongly extrapolate it forward.