Digital computation Punched tape programs would be much longer than the short fragment of yellow paper tape shown. The era of modern computing began with a flurry of development before and during World War II, as electronic circuit elements replaced mechanical equivalents and digital calculations replaced analog calculations. Machines such as the Z3, the Atanasoff–Berry Computer, the Colossus computers, and the ENIAC were built by hand using circuits containing relays or valves (vacuum tubes), and often used punched cards or punched paper tape for input and as the main (non-volatile) storage medium. In this era, a number of different machines were produced with steadily advancing capabilities. At the beginning of this period, nothing remotely resembling a modern computer existed, except in the long-lost plans of Charles Babbage and the mathematical ideas of Alan Turing. At the end of the era, devices like the Colossus computers and the EDSAC had been built, and are agreed to be electronic digital computers. Defining a single point in the series as the "first computer" misses many subtleties (see the table "Defining characteristics of some early digital computers of the 1940s" below). Alan Turing's 1936 paper proved enormously influential in computing and computer science in two ways. Its main purpose was to prove that there were problems (namely the halting problem) that could not be solved by any sequential process. In doing so, Turing provided a definition of a universal computer which executes a program stored on tape. This construct came to be called a Turing machine; it replaces Kurt Gödel's more cumbersome universal language based on arithmetics. Except for the limitations imposed by their finite memory stores, modern computers are said to be Turing-complete, which is to say, they have algorithm execution capability equivalent to a universal Turing machine. Nine-track magnetic tape For a computing machine to be a practical general-purpose computer, there must be some convenient read-write mechanism, punched tape, for example. With a knowledge of Alan Turing's theoretical 'universal computing machine' John von Neumann defined an architecture which uses the same memory both to store programs and data: virtually all contemporary computers use this architecture (or some variant). While it is theoretically possible to implement a full computer entirely mechanically (as Babbage's design showed), electronics made possible the speed and later the miniaturization that characterize modern computers. There were three parallel streams of computer development in the World War II era; the first stream largely ignored, and the second stream deliberately kept secret. The first was the German work of Konrad Zuse. The second was the secret development of the Colossus computers in the UK. Neither of these had much influence on the various computing projects in the United States. The third stream of computer development, Eckert and Mauchly's ENIAC and EDVAC, was widely publicized. George Stibitz is internationally recognized as one of the fathers of the modern digital computer. While working at Bell Labs in November 1937, Stibitz invented and built a relay-based calculator that he dubbed the "Model K" (for "kitchen table", on which he had assembled it), which was the first to calculate using binary form. Zuse Z1 (computer), Z2 (computer), Z3 (computer), and Z4 (computer) A reproduction of Zuse's Z1 computer Working in isolation in Germany, Konrad Zuse started construction in 1936 of his first Z-series calculators featuring memory and (initially limited) programmability. Zuse's purely mechanical, but already binary Z1, finished in 1938, never worked reliably due to problems with the precision of parts. Zuse's later machine, the Z3, was finished in 1941. It was based on telephone relays and did work satisfactorily. The Z3 thus became the first functional program-controlled, all-purpose, digital computer. In many ways it was quite similar to modern machines, pioneering numerous advances, such as floating point numbers. Replacement of the hard-to-implement decimal system (used in Charles Babbage's earlier design) by the simpler binary system meant that Zuse's machines were easier to build and potentially more reliable, given the technologies available at that time. Programs were fed into Z3 on punched films. Conditional jumps were missing, but since the 1990s it has been proved theoretically that Z3 was still a universal computer (ignoring its physical storage size limitations). In two 1936 patent applications, Konrad Zuse also anticipated that machine instructions could be stored in the same storage used for data—the key insight of what became known as the von Neumann architecture, first implemented in the British SSEM of 1948. Zuse also claimed to have designed the first higher-level programming language, (Plankalkül), in 1945 (published in 1948) although it was implemented for the first time in 2000 by a team around Raúl Rojas at the Free University of Berlin—five years after Zuse died. Zuse suffered setbacks during World War II when some of his machines were destroyed in the course of Allied bombing campaigns. Apparently his work remained largely unknown to engineers in the UK and US until much later, although at least IBM was aware of it as it financed his post-war startup company in 1946 in return for an option on Zuse's patents. Colossus Colossus was used to break German ciphers during World War II. During World War II, the British at Bletchley Park (40 miles north of London) achieved a number of successes at breaking encrypted German military communications. The German encryption machine, Enigma, was attacked with the help of electro-mechanical machines called bombes. The bombe, designed by Alan Turing and Gordon Welchman, after the Polish cryptographic bomba by Marian Rejewski (1938), came into use in 1941. They ruled out possible Enigma settings by performing chains of logical deductions implemented electrically. Most possibilities led to a contradiction, and the few remaining could be tested by hand. The Germans also developed a series of teleprinter encryption systems, quite different from Enigma. The Lorenz SZ 40/42 machine was used for high-level Army communications, termed "Tunny" by the British. The first intercepts of Lorenz messages began in 1941. As part of an attack on Tunny, Professor Max Newman and his colleagues helped specify the Colossus. The Mk I Colossus was built between March and December 1943 by Tommy Flowers and his colleagues at the Post Office Research Station at Dollis Hill in London and then shipped to Bletchley Park in January 1944. Colossus was the first totally electronic computing device. The Colossus used a large number of valves (vacuum tubes). It had paper-tape input and was capable of being configured to perform a variety of boolean logical operations on its data, but it was not Turing-complete. Nine Mk II Colossi were built (The Mk I was converted to a Mk II making ten machines in total). Details of their existence, design, and use were kept secret well into the 1970s. Winston Churchill personally issued an order for their destruction into pieces no larger than a man's hand. Due to this secrecy the Colossi were not included in many histories of computing. A reconstructed copy of one of the Colossus machines is now on display at Bletchley Park.