Like Atanasoff, Stibitz was known as a tinkerer. It was therefore not surprising to his colleagues that when in November 1937 he built his Complex Number Calculator, he named it the “Model K”; “K” stood for kitchen, because, he said, it was based on electromagnetic relays (not the same as the devices Zuse calls relays)—flashlight bulbs, a dry cell battery, and some metal strips he cut from a tin can—that he found and put together in his kitchen. The relays Stibitz was using were ubiquitous in telephone technology, and Stibitz’s calculator operated by triggering relays representing different decimal numbers—the activation of a 3 and a 4 triggered the activation (switching to “on”) of the switch representing 7. Stibitz also figured out how to use the telephone system to activate his relays from a distance—in 1940, he would use a teleprinter (similar to a teletype machine) at Dartmouth College in New Hampshire to send a calculation to his computer in New York and to receive the solution. The most ambitious attempt was Howard Aiken’s developing project at Harvard, with IBM, but Atanasoff knew that it was completely different from what he was attempting.
Once Atanasoff and Berry began, they moved right along—they had a “breadboard” prototype ready to test in October 1939—that is, it consisted of a breadboard-sized piece of wood on which Berry had built an electrical system of eleven vacuum tubes and fifty capacitors (or condensers, as they were called). According to Atanasoff, “It could just add and subtract the binary equivalents of decimal numbers having up to eight places” (anything up to 99,999,999 depending on the placement of the decimal point) but it worked, and it worked in accordance with Atanasoff’s four original principles. And it was frugal in every way. Atanasoff demonstrated the prototype for college officials a few weeks later and received further funding—$110 for more materials and $700 for other expenses.1
Even so, and this would prove the world’s boon and Atanasoff’s bane (and also prove Aiken’s precept about having to ram good ideas down people’s throats), Iowa State officials and Atanasoff’s own colleagues didn’t show much understanding or enthusiasm. The machine itself was unprepossessing, and no one was as familiar with its innovative nature or its limber technological possibilities as Berry and Atanasoff were. Those who wandered down into the basement to have a look sometimes made dismissive remarks, and the college was “supportive” in terms of hundreds of dollars, not thousands of dollars (IBM was soon spending half a million dollars on Aiken’s prototype). At the same time, Atanasoff owed his ideas to no one—there was no government agency or corporate committee that he had to explain his ideas to, no one he might offend by throwing out decades or centuries of common wisdom about calculating. Because he was frugal, he was free to think in innovative ways. What Atanasoff’s fellow professors could not see was that the breadboard calculator incorporated seven innovations:
Electronic computing
Vacuum tubes as the computing mechanism and operating memory
Binary calculation
Logical calculation
Serial computation (each step followed a previous one)
Capacitors as storage memory
Capacitors attached to a rotating drum that refreshed the power supply of the vacuum tubes and maintained (or refreshed, jogged, regenerated) the operating memory
Since he was well aware of Babbage’s Analytical Engine, and thought that the English mathematician had foundered because he was too ambitious, Atanasoff’s next decision was to limit himself to devising a machine for the solution of linear equations rather than to attempt to invent a universal machine. It was the differential equations that had made Atanasoff’s dissertation so tedious in 1930, but more important, even though both Atanasoff and Berry saw the grander implications of the breadboard calculator, they had money only for the next step. The differential equations were converted to “finite difference” equations—these were the equations their computer would be able to solve, equations containing up to twenty-nine unknowns. Such a capacity would almost triple the limit of ten unknowns that was then considered possible in solving systems of equations.
The construction of the new prototype began in January 1940, when Clifford Berry started cutting the angle iron to be used in the larger machine. In the meantime, Atanasoff himself took on a second, war-related project, which was to invent a method of predicting the movement of artillery targets and to invent a device that could perform such accurate tracking. Atanasoff hired another graduate student, Sam Legvold, and took over an area near the computer area in the basement of the physics building. What enabled Atanasoff to take on this extra work (in addition, of course, to his exceptionally energetic nature) was the fact that Berry fully understood the computer they were building, and he had assumed not only most of the construction work, but also responsibility for many of the adjustments and improvements that had to be made. The most important thing, though, was that the vacuum tubes had to work reliably. After Atanasoff and Berry ascertained this by testing in January 1940, the project moved quickly and the machine was constructed and ready to test within a few months.
Once his paper “On Computable Numbers” was completed and published in the spring of 1936, Alan Turing’s world expanded again—by the end of that September, he was at Princeton, enjoying (or not) a graduate fellowship there and meeting some of the best mathematical minds in the world. He wrote home in October with a list of those who were around: John von Neumann, Hermann Weyl, Richard Courant, G. H. Hardy, Albert Einstein, Solomon Lefschetz, and Alonzo Church. He regretted having missed Kurt Gödel, who had been there the year before, and perhaps Paul Bernays (of whom he was a bit disdainful—Turing was feeling more and more self-confident). Hardy, whom he knew from Cambridge, was friendly, but Turing found the way Americans talked unpleasant and Princeton disconcerting—casual and familiar, if sometimes fun (an impromptu hockey team of which Turing was a member went to Vassar and played an entertaining game with another impromptu team of girls). “On Computable Numbers” was published in January, but the response was disappointing—only two people asked for offprints. In many ways, even though he was at the most important nexus of mathematics in his time, he was too shy to push himself forward and make connections. Even Alonzo Church subsequently remembered very little about him. At the end of the year, Turing applied for an appointment at Cambridge but failed to get it, so he applied for another fellowship at Princeton—John von Neumann was one of his referees and gave him an excellent recommendation, but in his letter he gave no sign that he had read or even was aware of “On Computable Numbers.” Turing spent the summer of 1937 back in England and returned to Princeton in the fall, and there he went into the Princeton workshop and built a small binary calculator.
Although he had written “On Computable Numbers” in binary terms (the marked and unmarked squares on the infinite paper tape fed into the computer could be 1s and 0s), he had not done so as part of the theory of the imagined computer, only as part of its mechanism. In the Princeton workshop, though, he saw the possibilities of binary numbers (and Boolean logic) in the use of relay switches for calculating multiplication problems (as Zuse also saw), and he even made his own relays, since they were no more available in Princeton, New Jersey, than they were in Berlin. Andrew Hodges writes, “The idea would be that when a number was presented to the machine, presumably by setting up currents at a series of input terminals, the relays would click open and closed, currents would pass through, and emerge at output terminals, thus in effect ‘writing’ the enciphered number.” He also addressed the Riemann zeta function, a problem in mathematics that is still unsolved, which concerns very large numbers. What Turing thought of was the movement of waves—and he remembered a device he had seen called the Liverpool tide-predicting machine, an analog machine invented first in the 1920s and then subsequently improved several times in the late 1930s, that used strings and pulleys to predict tides in the river Mersey. It worked by measuring, not counting, but its measurements added up as the machine operated day after day, year after year. Turing wondered if a
machine built according to similar principles could be used for zeta-function calculation.
Most important, Turing wrote his PhD thesis, which addressed Gödel’s incompleteness theorems. His thesis adviser was Alonzo Church, who seems to have felt some rivalry with Turing stemming from the nearly simultaneous appearance of his lambda calculus and Turing’s computable numbers paper. Gödel’s incompleteness theorems amounted to a pair of rules that limited the aspiration of mathematics to make an understandable system out of the world of numbers. The first theorem states that no system can be both consistent and complete. The second states that any theory that contains basic arithmetical truths and also certain truths about formal provability will include a statement of its own consistency if and only if the theory is inconsistent. Turing’s thinking on this subject was an extension of his thinking in “On Computable Numbers,” and he passed his PhD examination at the end of June 1938. According to David Leavitt, the problem for pure mathematics at this time was to limit the implications of Gödel’s theorems, so that they “should interfere as little as possible with the practice of mathematics.” Turing’s ideas supported Gödel’s theorems, and subsequently Gödel seems to have approved of them more than he approved of Church’s similar but differently formulated lambda calculus. Twenty-six when he took his PhD exam, Turing was gaining a reputation as a mathematician. John von Neumann, who by now appears to have read “On Computable Numbers,” was impressed enough to offer Turing a lucrative position ($1,500, about $22,000 in 2010 dollars) as compared to the $800 Atanasoff had received ten years earlier at Iowa State) as his assistant at Princeton for the academic year 1938–39, but Turing missed England and went home, even though he had no position waiting for him (as far as we know).
By 1937, British Intelligence knew that the Germans were using an encoding system called Enigma that, except in minor ways, they could not break. When Turing returned from Princeton, he enrolled in a course about codes and code breaking given by the Government Code and Cypher School. How long he had been in contact with British intelligence, who initiated the contact, and what Turing’s motives for enrolling were remain unclear, but by 1938, after the union of Germany and Austria, it was clear that the world was a dangerous place, and England had to begin to act to protect itself. The dangers were brought home to Turing in a very personal way after he got back to England, when a friend of his was contacted by a woman the friend had known in Vienna. In the fall of 1938, the woman’s two sons turned up in a refugee camp at Harwich. Turing went with his friend to meet the boys and decided to sponsor the schooling of another boy he met there, Bob Augenfeld, who was sent to a boarding establishment in Lancashire. He also continued with the code-breaking school, and in the spring of 1939, he went back to Cambridge to give a lecture course himself for undergraduate students preparing for their final exams and to take a course from Ludwig Wittgenstein, during which they discussed, and disagreed upon, the idea that mathematics could be a logical system whether or not it was a “true” system. Wittgenstein persisted in thinking that there was value in a logical system even if it did not work in the real world; Turing disagreed. Turing also began thinking again about the Liverpool tide-predicting machine. The machine Alan Turing was thinking of (and received forty pounds sterling to develop) would use weights and counterweights attached to rotating gears to set up problems. Their solutions would be measured by a comparison of weights—an analog idea. Turing and a colleague worked on this machine in their office at Cambridge through the summer of 1939, but in the fall, after the German invasion of Poland, Turing went to Bletchley Park to aid in the breaking of the Enigma.
Yet another, and still more obscure, inventor of the computer, one whom Alan Turing would soon know very well, was Tommy Flowers. He was an engineer at the General Post Office Research Station at Dollis Hill in northwest London (not far from Hampstead Heath). At the end of August 1939, Flowers was in Germany. In an eerie parallel to Zuse’s experience with friendly English students just before the outbreak of the war, he recalled, “I was in Berlin on laboratory business only days before hostilities began. A telephone call from the British Embassy made me go home at once, and I crossed the border into Holland only hours before the German frontier was closed.” Flowers was the engineer Turing would work with during the war, and the fates of the two men, with regard to the invention of the computer, were deeply entwined, but no biographies or plays have been written about Flowers, nor did he write his autobiography, so how he viewed his career has to be inferred from a very few sources. His obituary on the BBC website is somewhat detailed:
Thomas Harold Flowers was born in London on 22 December, 1905. He seems to have been a practical child, when told of the arrival of a baby sister he declared a preference for a ‘Meccano’ set. After school, he embarked on a four-year apprenticeship in Mechanical Engineering at the Woolwich Arsenal and went to night classes to study successfully for a degree in Engineering from London University.
After graduating, he joined the General Post Office (GPO), which was then responsible for all telecommunications within the UK. He worked at Dollis Hill, the GPO’s research station, on experimental electronic solutions for long-distance telephone systems. In the 1930s, that meant thermionic valves [known as “vacuum tubes” in the United States], which were seen more as analog amplifiers than electronic switches. These would replace or enhance the electro-mechanical switches then used. These experiments formed the basis for modern direct dialing, but that was some way off. His work also drew the attention of others with quite a different purpose in mind.
With easier access to such tubes than either Atanasoff or Zuse, Flowers did an experiment in 1934 in which he wired together three to four thousand vacuum tubes that controlled a thousand lines, and communicated by means of tones. Like Zuse, Flowers encountered resistance from his superiors on the score of reliability, but in 1939 his system was introduced in a limited fashion.
Flowers later expressed strong opinions about the essential value of what he invented and built to the British war effort. It is also clear that he was the very engineer that Turing needed to realize his own computing ideas, but it was not until 2006 that even the outline of Flowers’s work came to be generally known. In the fall of 1939, he was just a thirty-three-year-old engineer with some insights into vacuum tubes who happened to escape from the Third Reich at the very last minute.
A reconstruction of Atanasoff and Berry’s second prototype is now on loan to the Computer History Museum near San Jose (as of summer 2010), though it normally resides in Atanasoff Hall at Iowa State University. The original was junked in 1948, with the permission of the chairman of the physics department, by a physics graduate student looking for office space (the replica was built in the 1990s by a team headed by computer scientist John Gustafson).2 Atanasoff and Berry worked on it through 1940, and Berry worked on it until June 1942. The frame of the computer (now known as the ABC, or the Atanasoff-Berry Computer) was seventy-four inches long, thirty-six inches deep, and about forty inches tall (including casters). Berry used the angle iron to construct a table with two levels, one about four inches off the floor that contained the boards holding the vacuum tubes and capacitors, which stood upright and faced front, along with several other components, including two transformers and a power supply regulator. Above that, at the back of the top table were two drums, each about eleven inches long and eight inches in diameter, several mechanisms for transposing binary numbers into and out of decimals, and a mechanism for charring holes in cards and feeding them back into the drums.
Solving twenty-nine linear equations with twenty-nine unknowns was still a lengthy process (taking some thirty hours) and required systematic inputs by the human operator, but it could be done, and the machine was accurate. In the first step of the process, the binary input unit converted each of the equations from decimal form to binary form and entered the equations on the input memory drum. Atanasoff had decided to use a variation of the punch-card system to input his equations and
to read out the results of the computer’s calculations, but he wanted to use an electronic method to mark the punch cards. The punch-card systems then available were based on decimal numbers, so he had to devise something new. What he decided to do was have the output component use an electric spark to burn a mark onto the card in a manner similar to a hole being punched—a spot charred into a space on the grid represented a 1. An empty space represented a 0. This mechanism proved more unreliable than the other mechanisms he had come up with for the calculating operations themselves—producing an inaccurate result (on a card) less than once in every ten thousand times, but more than once in every hundred thousand times. The ABC itself was successful, though, and demonstrated that Atanasoff’s ideas with Berry’s tweaks and construction could perform many more sorts of calculations than the one Atanasoff and Berry had designed it to do. Apart from the card issue, the ABC was operational by mid-1940.
In a thirty-five-page manuscript that Atanasoff completed in August, he described the ABC in detail. He listed the nine sorts of linear algebraic equations he thought a larger machine would be able to solve (see this page, footnote) and outlined their practical applications in physics, statistics, and technology. They ranged from problems of elasticity to approximate solutions of quantum mechanics problems. He expected the machine to be powerful and versatile, but he always conceived it as a machine for solving mathematical problems. In this, his ideas came to diverge, inevitably, from those Flowers and Turing would soon be contemplating.