Konrad Zuse, Who Built The First Programmable Computer And Then Argued The Universe Is One

Konrad Zuse was a German civil engineer who built the Z3 in wartime Berlin, the first working programmable automatic computer, and later argued that the universe is itself a computation. The second claim is the one that has outlived him. He made it in a short book called Rechnender Raum, published in 1969 and translated the next year as Calculating Space. In it he proposed that physics is what a very large cellular automaton does. Almost nobody in physics took it seriously at the time. The idea now sits under digital physics, under the simulation argument, and under every discussion of what a quantum computer is actually doing when it simulates matter.

Zuse is an awkward figure, and the awkwardness is worth stating early. He built machines for the German air ministry during the war, his best work was destroyed by Allied bombs, and his most original idea was one he could not make work. He knew he could not make it work. The most interesting thing in Calculating Space is not the thesis. It is the list of objections Zuse raised against himself, most of which are still the objections today.

The engineer who wanted to stop doing arithmetic

Zuse was born in Berlin on 22 June 1910 and studied at the Technische Hochschule Berlin-Charlottenburg, now the Technical University of Berlin. He started in mechanical engineering, moved to architecture, and finished with a civil engineering degree in 1935, by the record of the IEEE Computer Society. He then took a job as a structural engineer at the Henschel aircraft works at Schoenefeld outside Berlin, where the work was long tables of repetitive arithmetic done by hand.

That is the whole origin of the machines. A structural engineer in 1935 spent his days evaluating the same formulae over and over with different numbers, and Zuse wanted the tedium automated. He left the job and set up a workshop in his parents’ flat. The Konrad Zuse Internet Archive records that he quit aircraft construction in 1936 to build the Z1. His parents let him use the living room.

He did not arrive from mathematical logic, and it shows in the order he worked. Working on his first computer in the late 1930s, he rediscovered propositional calculus by himself, and only then learned it had a name.

The Z1, the Z3 and what the word first is worth

The Z1 was finished in 1938 and was entirely mechanical. It was built from thin metal sheets cut with a jigsaw, driven by an electric motor at about one cycle a second, and read its program from holes punched in 35 mm film. It worked in binary floating point, which was unusual and correct, but it jammed constantly, because thousands of sliding metal plates have to stay in step and they did not.

Money came from his family, his sister Lieselotte, friends in the AV Motiv student society, and Kurt Pannke, a Berlin manufacturer of calculating machines. The Z2 followed in 1940 and replaced the mechanical arithmetic with telephone relays. The Z3 followed in 1941. It used relays throughout, ran at about five cycles a second, worked to 22 binary digits in floating point, and took its program from punched tape.

Zuse presented the Z3 on 12 May 1941 to an audience that included Alfred Teichmann and Curt Schmieden of the German aviation research institute. That institute used the machine for statistical analysis of wing flutter. This is the machine behind the first claim. The careful version of that claim is that the Z3 was the first programmable, automatic, digital computer that actually worked, and every word in it is load bearing.

What the Z3 was not is equally important. It was not electronic, since it switched relays rather than valves. It did not store its program in memory, so it read instructions off a tape as it went. Loops were managed by joining the two ends of the punched tape together, and there was no way at all to make the machine choose between two courses of action. Raul Rojas put it plainly in 1997, writing that “the Z3 is therefore not a universal computer in the sense of Turing”. A year later he showed that the Z3 is in principle Turing complete after all. The proof works only through a trick that computes every possible outcome of a decision and then throws away the ones not wanted. That is a statement about what the architecture permits, not a description of how anyone programmed the machine in 1941.

What the war took, and what Zuse built for it

From 1939 the German aviation research establishment paid for his work, and the work was weapons. Zuse built two special purpose machines, the S1 and the S2, which computed aerodynamic corrections for the wings of radio-controlled flying bombs. Those bombs were the Henschel Hs 293 and Hs 294, the ancestors of the guided missile.

Zuse never joined the Nazi Party and is not recorded as having objected to any of this at the time. Long afterwards he described the position of a scientist under such a state as a bargain with the devil, in which the alternative to questionable work is no work. It is not a defence and he did not offer it as one.

The bombing took nearly everything. His workshop on Methfesselstrasse, with the Z3 inside it, was destroyed in an Allied raid on 21 December 1943. His parents’ flat, with the Z1 and the Z2, was destroyed on 30 January 1944. Only the unfinished Z4 survived, because it was in different premises, and in February 1945 it was carted out of Berlin to Goettingen ahead of the Soviet advance.

The Z4 is the one machine of his that you can still see in the metal, and it went to ETH Zurich in 1950 and ran there until 1955. It was then sold to a Franco-German research institute at Saint-Louis, and in 1960 it came back to the Deutsches Museum in Munich. It has a reasonable claim to be the oldest surviving programmable computer, and a second reasonable claim to be the world’s first commercial digital computer.

Plankalkuel, a language with nowhere to run

Stuck in the Bavarian Alps after the war with no parts and no permission to build, Zuse designed a programming language instead. He worked on Plankalkuel between 1942 and 1945. It had assignment, subroutines, conditional statements, loops, floating point arithmetic, arrays, record structures and exception handling, at a time when the rest of the world was still wiring plugboards. He wrote pieces of a chess program in it.

The publication history is dismal. He got short excerpts into print in 1948 and 1959, and the complete work stayed unpublished until 1972. By then Fortran, ALGOL and COBOL had been designed without it, and Zuse was openly disappointed that the ALGOL 58 committee never acknowledged any debt. The usual claim for Plankalkuel is that it was the first high-level programming language designed for a computer, and it holds up.

One detail is routinely got wrong. Plankalkuel was compiled during Zuse’s lifetime. Joachim Hohmann built the first compiler for it in a 1975 dissertation, twenty years before Zuse died, and further independent implementations followed in 1998 and in 2000 at the Free University of Berlin. What is true is that Zuse never implemented it on any of his own machines. The language and the hardware never met.

Zuse KG, 251 machines and a sale to Siemens

Zuse founded Zuse KG in November 1949 at Haunetal-Neukirchen, and moved the head office to Bad Hersfeld in 1957. The company sold the Z11 to the optics industry and to universities, built the Z22, and made a drawing machine called the Graphomat Z64. Across his working life Zuse built 251 machines.

It did not survive him, because growth outran the money, deliveries of the Z25 ran late, and in 1964 Zuse had to give up his shareholding to Brown, Boveri of Mannheim. Siemens took the company over from them at the beginning of 1967.

The patents went the same way. Zuse filed an application in 1941 covering the Z3, it was finally published in 1952, and both Triumph and later IBM opposed it. The case ground through every level of the German courts until 1967, when the Federal Patent Court refused it for lack of inventive step. The man generally described as having built the first working computer lost the patent on it in the same year he lost the company.

Rechnender Raum, and what Zuse actually argued

The idea arrived in 1945 or 1946, in Hinterstein, during the same enforced idleness that produced Plankalkuel. Zuse published a paper called Rechnender Raum in the journal Elektronische Datenverarbeitung in 1967, and the book of the same name with Vieweg in 1969. MIT’s Project MAC had it translated into English by February 1970 as Calculating Space, and that translation is the version most people have read. The quotations below come from that translation, in the 2012 re-edition by Adrian German and Hector Zenil.

The argument runs in one direction throughout. Physics is written in differential equations, differential equations are approximated by difference equations when you compute them, so ask what happens if the difference equations are not an approximation but the thing itself. Space becomes a grid of cells. Each cell holds a small whole number. Each cell updates from its neighbours by a fixed rule, at a fixed tick, forever.

Zuse called the stable travelling patterns in such a grid digital particles, and he spent most of the book building small examples by hand and watching what they did. Two of them collide and pass through each other, or fail to, or come apart. He named the formalism explicitly, citing von Neumann’s work on self-reproducing automata, and the fourth chapter of the book is headed with cellular automatons and digital particles. The last line of the conclusions is the honest one. “It must be stressed that the experiments of the author are confined to pen and paper experiments.”

Determinism is the load the whole structure carries. Zuse argued that an automaton is determined in the positive time direction only, because the rule tells you the next state and nothing tells you the previous one. He thought this was a feature rather than a defect, and that classical physics had quietly assumed something far more expensive. A model exact in both time directions needs infinite precision everywhere. As he put it, “simulations of universal systems with causality functioning in both time directions belong to the category of unsolvable problems.” Then he asked the question that the entire field has been arguing about since. “Are we justified in assuming a model of nature for which no calculable simulation is possible?”

Where Zuse got stuck, and knew it

Quantum mechanics is the problem with a deterministic cellular automaton, and Zuse said so himself, in his own book, setting out the difficulty in the second chapter and never resolving it. “It will be extremely difficult to find a technical model of a hybrid computer which behaves according to the laws of quantum physics.” Summaries of Zuse leave this out and present him as claiming more than he claimed.

He did try. He offered a reading of the uncertainty principle in terms of information, with a fixed budget of bits shared between two quantities, so that giving one more precision leaves the other with less. He noticed that his digital particles pass through phases in which their position is not defined between ticks, and asked whether that resembled the relation between position and momentum. His own verdict on the resemblance was sceptical. “In any case the computer model, in spite of the apparent error, is characterized by strict predetermined happenings.”

On randomness he was sharper still. A computer can only fake it, either by generating pseudo-random numbers from a rule or by taking real ones from a physical process such as radioactive decay. “It remains true, however, that real probability values are hardly possible in technical automatons.” Whether nature is allowed genuine randomness he refused to answer. “This question is a philosophical one, and is only noted here, without an answer.”

Calculating Space ends with a table of three columns, one for classical physics, one for quantum mechanics and one for his own proposal. Where the quantum column meets his own, Zuse wrote a question rather than a claim. “Are the limits of probability of quantum physics explainable with determinate space structures?” That is a research proposal and not a result. He listed three possible responses to his own book, and the first was that the ideas contradict recognised physics and the foundation must therefore be false.

He saw the other objection too, decades before it was proved. A regular grid picks out directions, so “a grid structure would abolish the isotropy of space.” A grid also picks out a frame, which special relativity forbids. Zuse wrote that “in any representation of the cosmos as cellular automatons, it is almost impossible to avoid the assumption of a superior system of movement.” He guessed the grid would be too fine to detect, and left it at that.

Who picked the idea up

Edward Fredkin named the field. He taught a graduate course at MIT under the title digital physics in 1978, and later preferred the term digital philosophy. With Tommaso Toffoli he built the technical core of the field in 1982, around reversible computing and what the two of them called conservative logic. His 1990 paper in Physica D proposed physics as a reversible universal cellular automaton. Fredkin is usually described as having reached the position independently, and none of his own accessible writing credits Zuse. He was director of MIT’s Project MAC from 1971 to 1974, and Project MAC is the group that had Calculating Space translated in 1970, which is an adjacency and not evidence.

Stephen Wolfram credits him directly. The index of A New Kind of Science carries an entry reading “Zuse, Konrad (Germany, 1910-1995) and universe as CA, 1026”. The note on that page says that “Konrad Zuse suggested that it could be a continuous cellular automaton; Edward Fredkin an ordinary cellular automaton.” Wolfram’s own hypergraph rewriting project descends from the same idea with the fixed lattice removed.

John Wheeler is the odd one out. His slogan it from bit is quoted in every popular account of digital physics, and his 1989 paper puts it plainly. “It from bit symbolizes the idea that every item of the physical world has at bottom, at a very deep bottom, in most instances, an immaterial source and explanation.” That paper does not cite Zuse. Its first stated conclusion is that the world cannot be a giant machine ruled by any preestablished continuum physical law, which is close to the opposite of Zuse’s thesis.

Seth Lloyd cites Zuse and then disagrees with him. His 2002 paper in Physical Review Letters put a number on the computation, bounding the universe at about ten to the power 120 elementary operations on about ten to the power 90 bits. His 2006 book Programming the Universe moved the substrate from bits to qubits. His 2013 essay lists Rechnender Raum in the references, poses the question “is the universe a cellular automaton”, and answers it in one word. His answer is no.

Nick Bostrom belongs to a different argument entirely. The 2003 simulation argument is a statistical claim about how many observers are simulated, and it does not require the world to be discrete. The text does not mention Zuse anywhere. Conflating the two is the commonest error here, and it is the distinction we drew in our profile of Rizwan Virk. Juergen Schmidhuber has done most to keep the attribution straight, writing on his page on Zuse’s thesis that “Zuse was the first to propose that physics is just computation.”

What physicists say now

The programme has not produced a confirmed novel prediction, and that is the first thing to say. What it has produced is a set of no-go results that sharpen exactly the two problems Zuse raised against himself, and neither problem has gone away. Neither should be softened in the telling.

The first is symmetry. Tobias Fritz proved in 2013 that for a particle hopping one edge per timestep on any periodic graph, the set of reachable velocities forms a polytope, and a polytope has corners. Corners are preferred directions. In his words, “since a polytope necessarily has distinguished directions, there is no periodic graph for which this velocity set is isotropic.” Sabine Hossenfelder showed in 2015 that there are no Poincare-invariant networks with a locally finite distribution of nodes in flat spacetime of any dimension. Zuse’s grid really does break the symmetries of relativity, as he suspected it would.

The second is Bell. A deterministic classical cellular automaton is a local hidden-variable theory, and that is the exact class of theory that Bell tests rule out. Hensen and colleagues closed the last experimental loopholes in 2015. They put two electron spins 1.3 km apart and measured 2.42 plus or minus 0.20, where any local hidden-variable theory is capped at 2. Scott Aaronson had already made the argument against Wolfram’s version in 2002, concluding that the proposal “cannot be made compatible with both special relativity and Bell inequality violation.”

Defenders have three replies and all three cost something. Gerard ‘t Hooft accepts the automaton and denies that experimenters can choose their settings independently of the hidden variables. That position is called superdeterminism, and many physicists regard it as buying determinism at the price of experiment itself. Others point out that quantum cellular automata are discrete and local yet are not hidden-variable theories, so Bell does not touch them. That reply works, and it concedes the original point, because the substrate it saves is made of qubits rather than bits.

Observation has started to bite as well. A discrete spacetime generally makes the speed of light depend on energy. Fermi’s measurement of a 31 GeV photon from the gamma-ray burst GRB 090510 pushed any such linear effect past the Planck scale. Beane, Davoudi and Savage worked the other end, deriving a bound on the spacing of any simulation lattice from the cutoff in the cosmic ray spectrum. The question is no longer purely philosophical, which is more than Zuse got in his lifetime.

What is left

The hardware survives better than the theory. A replica of the Z3 built by Zuse KG in 1961 stands in the Deutsches Museum in Munich next to the original Z4. Zuse rebuilt the Z1 himself between 1987 and 1989, at a cost of 800,000 Deutschmarks and a heart attack partway through, and that machine is in the Deutsches Technikmuseum in Berlin. He died at Huenfeld in Hesse on 18 December 1995, and the Zuse Institute Berlin carries his name.

The theory is in a stranger position. Zuse asked whether the world can be computed exactly, and the answer that has emerged is that it probably can, but not by the kind of machine he built. Every serious route out of the Bell and isotropy objections runs through quantum information rather than classical bits. The live version of his question is Lloyd’s, whether the universe is a quantum computer.

That is a better fate than being forgotten, and it is better than having been right. Zuse posed a question precisely enough that physicists could later prove parts of his own answer wrong. He wrote in 1969 that his experiments were confined to pen and paper, and he was marking the boundary of what he had shown.

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