Humans and businesses alike evolved in a world that was local and linear. But today we live in a world that is global and exponential. The problem, say the authors, is that our brains-and thus our perceptual capabilities-were not designed to process at this scale or speed. Using the example of Kodak's downfall, they show that our linear minds literally cannot grasp 'exponential progression'. They present a framework called 'the Six Ds of Exponentials', which is designed to help today's leaders navigate 'the age of exponentials'-and avoid being disrupted.

The CEO of the X Prize Foundation explains how offering cash jackpots for breakthrough innovations can help solve problems big and small in fields like space exploration, energy, and education.