In Germany in 1936, Konrad Zuse added limited programming capability to a mechanical binary calculator. He is regarded by some as an inventor of the modern digital computer. Vannevar Bush had invented the analog computer in 1927. Bush called it a differential analyzer, an analog computer with some digital components that could solve differential equations. Zuse's Z1 components were simple digital switches he manufactured himself. Later machines, like the Z2 in 1039 used telephone relays. German army funding supported the Z2.

In May, 1941, Zuse finished the Z3, a binary 22-bit floating-point calculator featuring programmability with loops but without conditional jumps, with separated memory and a calculation unit. The Z3 was a Turing complete computer, though Zuse knew nothing of Turing. The Z3 was a floating-point machine. Howard Aiken's Mark I (at Harvard) and the ENIAC (at U Penn's Moore school were fixed-point.

For the Z4 (142-1945) Zuse developed the first computer programming language, Plankalkül (Plan-calculus). This was the first known formal system of algorithm notation, capable of handling branches and loops. In 1942 Zuse began writing a chess program in Plankalkül. This was four years before the ENIAC.

In later years, Zuse argued that the universe is a cellular automaton being computed by discrete computing machinery like his Z1. This was a few years before John Conway's "game of life" in 1970, perhaps the most famous example of cellular automata, and Stephen Wolfram's Mathematica.

Zuse thought that the laws of nature should be discrete and not continuous, that difference equations might describe the universe better than differential equations, as Einstein had speculated late in life. Zuse argued correctly that entropy and its growth do not make sense in deterministically computed universes.

This is correct. Information is a constant in a deterministic universe. But of course entropy and its increase is an established fact of the universe. There is far more entropy, as well as information, in the universe today than at its origin. The unstoppable growth of entropy superficially appears to conflict with the growth of information.

The macroscopic irreversibility of entropy increase depends on microscopic irreversibility, as Ludwig Boltzmann first argued, calling it "molecular chaos." Information increase similarly depends on the randomness of quantum physics, which provides the alternative possibilities needed for the creation of new information structures.

In the 1960's Zuse proposed that space itself is digital and that it could be "calculating the universe." He called this idea Rechnender Raum, or "Calculating Space." His work inspired a number of thinkers who are sometimes called "digital philosophers" or digital physicists" They include Gregory Chaitin, Edward Fredkin, Seth Lloyd, Rudy Rucker, Jürgen Schmidhuber, Stephen Wolfram, and Zuse.

Information structures can be described digitally. But it is not space itself that is digital. It is the arrangement in space of discrete particles of matter that constitutes an information structure.

And it is not an intrinsic discrete nature of space itself, but quantum limits on the occupation of space by particles, the Pauli exclusion principle, which says only a finite number of material particles are allowed in a given spatial volume, given the average energy per particle (i.e., the kinetic temperature).

There is no such limit on particles of energy, photons and other bosons.

Calculating Space