Turing's Cathedral: The Origins of the Digital Universe

by George Dyson

That two symbols were sufficient for encoding all communication had been established by Francis Bacon in 1623. “The transposition of two Letters by five placeings will be sufficient for 32 Differences [and] by this Art a way is opened, whereby a man may expresse and signifie the intentions of his minde, at any distance of place, by objects … capable of a twofold difference onely,” he wrote, before giving examples of how such binary coding could be conveyed at the speed of paper, the speed of sound, or the speed of light.3 That zero and one were sufficient for logic as well as arithmetic was established by Gottfried Wilhelm Leibniz in 1679, following the lead given by Thomas Hobbes in his Computation, or Logique of 1656. “By Ratiocination, I mean computation,” Hobbes had announced. “Now to compute, is either to collect the sum of many things that are added together, or to know what remains when one thing is taken out of another. Ratiocination, therefore is the same with Addition or Substraction; and if any man adde Multiplication and Division, I will not be against it, seeing … that all Ratiocination is comprehended in these two operations of the minde.”4 The new computer, for all its powers, was nothing more than a very fast adding machine, with a memory of 40,960 bits.