Reality+: Virtual Worlds and the Problems of Philosophy

by David J. Chalmers

In addition to inventing binary arithmetic, Leibniz himself designed and built some of the earliest mechanical calculating machines. The first such machine was designed by another great philosopher/mathematician, Blaise Pascal, in 1642. Pascal’s calculator performed addition and subtraction, and Leibniz’s (designed in 1671) performed multiplication and division as well. Their machines used dials encoding sequences of decimal digits rather than binary digits (Leibniz discussed a binary machine in his 1703 essay but never built it), but they process structural information all the same. This brings out that bits aren’t strictly required for structural information—sequences of decimal digits or even letters of the alphabet qualify too. Still, the core case of structural information remains sequences of bits.