Lloyd developed his formula because his work on quantum computers, which use single atoms to encode information and perform computations, had him thinking about the universe in terms of bits that live in atoms. He performed a thought experiment, asking himself: What is the largest computer that could ever be built? The answer: one that would employ every atom in the universe. That computer could store 1090 bits.

But the beauty of Lloyd’s formula is that it can be used to estimate the information-storing capacity of any physical system, not just the universe. Recently I have drawn inspiration from Lloyd’s formula while exploring the computational capacities of economies and societies. Lloyd’s formula does not incorporate much of the social and economic complexity inherent in our economies, but it gives us rough estimates of the capacity of sys- tems to store and process information. Think of Earth as a hard drive. According to Lloyd’s formula, the planet can store up to 1056 bits — roughly a trillion trillion trillion trillion gigabits. But is this planetary hard drive mostly empty or mostly full? ...