Atanasoff was now at Iowa State, where his primary responsibility was teaching, not research. Although he might have said that his first love was theoretical physics, or even quantum mechanics, Iowa State did not have a course in quantum mechanics until Atanasoff began teaching one. Atanasoff did have quite a few students, however, and teaching them reminded him over and over of the difficulties of calculation. By all accounts, Atanasoff was a gifted teacher who used an individualized Socratic approach, engaging his students in discussions and questioning them, trying to discover their areas of expertise and ignorance. He saw over and over that all scientific and engineering progress would be retarded until some sort of breakthrough in methods of calculation. He also employed his students in investigating ways of calculating. One of these students came up with an idea for a type of small analog calculator, something like a slide rule, that measured fourteen inches by three inches by three inches. Atanasoff, the student, and another colleague designed it to calculate the geometry of surfaces and called it a “Laplaciometer,” after the eighteenth-century French mathematician and astronomer Pierre-Simon Laplace, but its uses were limited.
Most calculators in the 1930s were analog, that is, they were similar to a slide rule in that something is measured in order to ascertain a number. As Atanasoff later explained to Clark Mollenhoff, his first biographer, the thing measured “can be anything: a distance, an electric voltage, a current of electricity, air pressure, etc.” Calculating ever larger numbers requires ever more sensitive measurements, so that, for example, a slide rule, which calculates numbers by measuring distance, would have to be enormous (“the length of a football field, or in some instances a mile or more”) in order to represent the numbers Atanasoff was interested in calculating.
One famous analog calculator that Atanasoff read about in the thirties was the Bush Differential Analyzer, developed in 1927–31 at MIT by Vannevar Bush, who had already founded the company that was to become Raytheon and would later head the National Defense Research Committee and the Office of Scientific Research and Development (which was in charge of what would become the Manhattan Project from 1941 until it was taken over by the army in 1943). The Differential Analyzer may be pictured as an automobile gearing mechanism used for calculation. It was “in essence a variable-speed gear, and took the form of a rotating horizontal disk on which a small knife-edged wheel rested. The wheel was driven by friction, and the gear ratio was altered by varying the distance of the wheel from the axis of rotation of the disk.” What was measured (as the slide rule measures distance) were the various positions of the shaft as it turned. These positions were assigned values like the numbers on a slide rule.
When, in 1936, Atanasoff and his colleagues decided that the possibilities of the Laplaciometer were limited, Atanasoff turned his attention to what might be done with the Monroe calculator, the same typewriter-like machine he had used at the University of Wisconsin when he was doing the math for his dissertation. The solution he thought up was similar to the mechanically based solutions others were trying, such as linking thirty machines and thereby enlarging their capacity. But enlarging capacity did not change the theory behind calculation—adding and subtracting remained the essential operations. Atanasoff did not have access to thirty machines, though. Instead, he got together with an Iowa State colleague, statistics professor A. E. Brandt, whom he had first met as a student in 1925. Brandt had access to a single IBM tabulator owned by the statistics department.
In the mid-1930s, IBM was a fairly new company, the product of several mergers, but having its origins in the Tabulating Machine Company, which had been founded in 1896 by inventor Herman Hollerith—his first model had been used in the census of 1900. In 1911, several companies joined to form the CTR (Computing Tabulating Recording) Corporation, which offered a wide range of services to businesses—calculating, but also timekeeping and meat-slicing (a product called the Dayton Safety Electric Meat Chopper—the division was sold to Hobart Manufacturing Company in 1934). Thomas J. Watson, Sr., had become president in 1915, and the name of the company was changed to International Business Machines in 1924. In 1928, IBM introduced the standard eighty-column punch card (the Hollerith card) that came to be familiar to students and secretaries for decades afterward. A 1931 model, developed for and used solely by the Columbia University Statistical Bureau to tabulate results of observations and experiments made at Columbia, seemed exciting at the time—one astronomer declared himself thrilled just watching how quickly the machine went through its additions and subtractions.
The less advanced device Atanasoff and Brandt decided to modify looked more like an upright piano than a desk calculator and operated in the customary Hollerith/IBM fashion, by reading a deck of punched cards and adding or subtracting the values represented by holes in the cards. With the help of IBM representatives, Atanasoff and Brandt modified the Iowa State–owned version of the tabulator in several significant ways and published an article about their product in 1936 in the Journal of the Optical Society of America entitled “Application of Punched Card Equipment to the Analysis of Complex Spectra.” It reads rather dryly, but what Atanasoff and Brandt were really doing was something Atanasoff had been doing since childhood—fiddling with a machine and redesigning it in order to get it to perform in a better or faster or more complex way. At the end of the article abstract is the line “The advantages of the method include high speed, accuracy as high as desired without checking with an adding machine, and the fact that only one simple modification is needed of standard equipment that is available almost everywhere.” According to Mollenhoff’s biography of Atanasoff, while IBM representatives cooperated with Atanasoff and Brandt in modifying the IBM calculator that they were using, IBM internal memorandums at the time were highly critical of Atanasoff and Brandt for “meddling with the tabulators and using them in ways the corporation officials had not intended that they be used.” According to Tammara Burton, who may have heard it from her grandfather, the memo said, “Keep Atanasoff out of the IBM tabulator.”
IBM was jealous of its intellectual property, something that another computer innovator was also discovering. If Atanasoff had ended up at Harvard, he might have met Howard H. Aiken (born March 8, 1900), whom he also might have met at the University of Wisconsin. Aiken, too, was eager to develop a calculating machine that would solve differential equations, and Aiken was not unlike Atanasoff in other ways—he had put himself through high school while working at the local electric company in Indianapolis and then through the University of Wisconsin (at precisely the same time that Atanasoff was putting himself through the University of Florida) by working at the gas company in Madison. After earning his bachelor’s degree, he worked in the private sector before going to the University of Chicago and then to Harvard for his master’s and his PhD. His dissertation, “Theory of Space Charge Conductions,” was similar to “The Dielectric Constant of Helium”—it considered “the properties of vacuum tubes—devices in which electric currents are passed across an empty space between two metal contacts.” Like Atanasoff, Aiken was exhausted by the calculations required to prove his thesis, or, as his biography puts it, “The mathematical complexities involved in describing space charge conduction made calculating solutions to his problems impossible.” While Atanasoff was pondering the Laplaciometer, Aiken, at Harvard, was trying to conceive of a way to improve Charles Babbage’s original Difference Engine. Harvard offered Aiken even less support than Atanasoff found at Iowa State College—in fact, President Conant actively discouraged him. Aiken then approached several mechanical calculating machine companies without success.
Most computer inventors in the 1930s, including Vannevar Bush and Howard Aiken, were convinced that the future of computing lay in its past—in the theories of Charles Babbage (1791–1871), who had begun laying out his ideas for a mechanical calculator in 1822 and proposed constructing it to the Royal Astronomical Society. It was an analog device, designed to solved polynomial equations using shafts and toothed gears. Babbage worked on it for twenty-five years, redesigning it at least once, but nineteenth-century machining wasn’t up to the precision of the task, and the Difference Engine never really worked. Even so, Babbage grew more ambitious and designed a machine he called the Analytical Engine. All of the twentieth-century computer inventors were aware of Babbage’s work (except Konrad Zuse, isolated in Germany). Howard Aiken proposed to update Babbage’s ideas with more modern industrial techniques—the machining of gears and shafts had advanced considerably in the hundred years since Babbage’s time. His Mark I was to be a relay-switch-based computer. And it was to be huge. It was to be built of
a power supply and electric motor for driving the machine; four master control panels, controlled by instructions on punched rolls of paper tape and synchronized with the rest of the machine; manual adjustments for controlling the calculation of functions; 24 sets of switches for entering numerical constants; 2 paper tape readers for entering additional constants; a standard punched card reader; 12 temporary storage units; 5 units each—add/subtract, multiply, divide; various permanent function tables (e.g. sine, cosine, etc.); accumulators; and printing and card punching equipment. All of these components should be built to accommodate figures up to 23 digits long. Finally, Aiken estimated the speed of the calculator based upon the speed of contemporary IBM machines, 750 8-digit multiplications per hour, representing a vast increase in speed and accuracy over manual methods of calculation.
It used a decimal number system, and even though Aiken had done his dissertation on vacuum tubes, his was a mechanical switching system.
At some point, perhaps reflecting on his efforts to get his computer built, Aiken is said to have remarked, “Don’t worry about people stealing your ideas. If your ideas are any good, you’ll have to ram them down people’s throats.” Perhaps in this, too, Aiken would have found a sympathetic listener in Atanasoff.
But Atanasoff was at least in a place where he could gather together the information he needed. Right around the time of the Laplaciometer, he discovered an electronic engineering textbook entitled The Thermionic Vacuum Tube and Its Applications, by Hendrik Johannes Van der Bijl, a South African physicist who had studied in Germany before returning to South Africa to design the national power grid and other state-sponsored enterprises. According to Burton, after reading Van der Bijl’s book, Atanasoff built some vacuum tubes on his own and began to think about novel ways he could put them to use.
A simple vacuum tube, called a diode, works like an incandescent lightbulb: a filament, called a cathode, is heated and then releases negatively charged electrons, which stream toward a positively charged metal plate, called an anode. The mechanism is enclosed within a tube of glass, which preserves the vacuum and disperses the heat generated by the filament. Numerous improvements in the diode were made throughout the beginning of the twentieth century, mostly for the purpose of improving radio design, reliability, and transmission. In 1936, the vacuum tube was used in radios to amplify transmission and reception of signals, and tubes continued to be used in radios and televisions until the invention of the transistor. The tubes were delicate and expensive to operate because of energy loss through the glass shell. But Atanasoff didn’t want his tubes to do much—he just wanted them to turn on and off. The measurement required by an analog calculator would be replaced by counting. Since this is similar to the way a child counts on his fingers, this came to be known as digital calculation.
The difference between measuring and counting, for Atanasoff’s purposes, was enormous: counting is precise, infinite, and as portable as an abacus. No quantities such as distance are involved, and no estimation needs to be made (as it does, for example, when the mark giving the result of a slide rule calculation falls between two marks indicating numbers). However, counting had its problems, too, since it is repetitive and mind-numbing. And for most of those attempting to invent the computer, the problem was that they themselves were used to counting in a base-ten (0–9) number system; there was no way to invent a simply constructed calculator that could do that. It is probably also true that the more that the inventors made use of mechanical calculators such as the Monroe, the more the idea of base-ten counting was reinforced, since a Monroe calculator consisted of a hundred black and white keys arranged in a ten-by-ten grid (using the digits 0–9), with red function keys set in two rows, across the bottom and down the right side as the operator faced the machine.
As a young man with a wife and young children, Atanasoff was busy at home as well as at school. Although faculty salaries were cut in the early 1930s as a result of the Great Depression, Atanasoff managed to get promoted quickly and to save up enough money to buy ten acres on Woodland Street, which runs due west from the ISU campus. He chose a plot for himself, designed a brick house, and oversaw its construction, moving his family into the basement in the summer after the February 1935 birth of his third child, a son named John Vincent II. Since Atanasoff believed in pay-as-you-go, progress on the house depended on ready cash. As a result, the family lived in the basement through the winter of 1935–36, protected from the cold and snow at times only by tarps and the floorboards of the partially constructed ground floor. Lura cooked in the laundry room. Atanasoff himself installed the electricity and plumbing, as well as the heating system for the baby’s room.
Shortly after the house was completed, Elsie, the older daughter, aged eight, became seriously ill with asthma and allergies. According to Burton, the standard treatment of the day, adrenaline shots, had a negative effect on Elsie’s condition, so Atanasoff threw himself into reading about allergies and observing his daughter. He decided that she was allergic to cow’s milk, chocolate, and wheat, and he bought two pregnant female goats, which Lura cared for and milked in the backyard of the Woodland Street house. He rigged up a system for circulating fresh air into Elsie’s room and became so knowledgeable about allergies that a local doctor used him as a consultant. His daughters also gave him entrée to the grammar school authorities—when teachers complained that the girls were often late because Atanasoff was dropping them off on his way to the college, he got interested in how the teachers were doing their jobs—investigated how school resources were being used and made suggestions about what the science and math curriculum should look like. When the school nurse suggested that one of the girls have her tonsils removed, Atanasoff lectured her on why they should not be removed. His arguments were always complete and forcefully presented, and school authorities soon learned to leave well enough alone. Once, Burton writes, “when the family’s enormous vegetable garden produced a large crop of soybeans, he immediately addressed the problem of shelling the beans by rigging the washing-machine clothes-wringer to assist in the task. Whole soybeans were hand-fed into the electric clothes wringer and came out shelled on the other side.”
But he worked late at the office, worked at home, and read the newspaper at the supper table. Home, like the office, was an arena for projects and creative thinking, not interaction, familial relationships, or leisure enjoyments—in fact, Atanasoff rather disdained pursuits such as art, music, and literature that Lura enjoyed. Lura understood Atanasoff’s pressing commitment to solving the problem of calculating, both as the inner drive to solve a problem creatively and as an essential scientific task. Burton indicates that Atanasoff’s frustration with the failures of the solutions he and his colleagues were coming up with in the mid-thirties was making him moody and hard to live with, but also that Lura’s own close-knit family of origin had not prepared her for the lonely life she found herself leading. Atanasoff was not happy. He wrote later, “I had been forced to the conclusion that if I wanted a computer suited to the general needs of science and, in particular, suited to solving systems of linear equations, I would have to build it myself. I was leading a full life and had too much to do; I did not want to search and invent, but sadly I turned in that direction.” He feared he would be wasting his best years on an endeavor that might prove fruitless. And he had no way of knowing who was inventing what in the world of computing or how his thinking fit into that of others—even if it worked, his invention could easily be preempted by another.
Like all land-grant universities, Iowa State was provincial and local, and intended to be so. Its obligations were to the state of Iowa, not to the larger worlds of industry or intellect. Atanasoff’s field was physics—he wanted a tool, and the tool was missing. It was characteristic of both his personality and his education that he decided to invent the tool, but it was also realistic on his part to fear that inventing the tool would be a waste of time he could be spending on other projects—his schedule was full and he had no real confidence that he could come up with the solution he sought.
Atanasoff spent 1936 and 1937 reading as much as he could about every calculator then in existence, and also about what other innovators thought possible. He also moved his office from the mathematics department to the new physics building, which was more spacious and more practically oriented. According to Burton, he felt that mathematics as a field was moving in the wrong direction—toward greater and greater abstraction—while physicists continued to be interested in concrete problems. In the meantime, Alan Turing was wrestling with similar dissatisfactions.
Alan Turing’s life at Sherborne was punctuated at the end with tragedy—in the winter of his last year (1930), his dearest friend, Christopher Morcom, died of tuberculosis. Morcom, slightly older and gifted with the star power that eluded Turing, had won many prizes at Sherborne, and then a scholarship to Trinity College. The two young men shared scientific and mathematical interests, and Turing profoundly respected not only Morcom’s intelligence, but also his thoroughness and his broad interests—he could play the piano and he could also do his work legibly without making arithmetical mistakes. Moreover, he was fun—among other pranks, he once sent gas-filled balloons over Sherborne Girls. It may have been Morcom’s positive influence that enabled Turing to get higher marks at Sherborne as he got closer to finishing his education there.
In 1931, Turing won his own scholarship to Cambridge, but to King’s College rather than Trinity. If, at the University of Florida and Iowa State, and even at the University of Wisconsin, Atanasoff was always more or less at the periphery of both the mathematics and physics establishments, at King’s College Turing was at the exact heart, especially of mathematics. He took courses from astrophysicist Arthur Eddington and mathematicians G. H. Hardy and Max Born. He met John von Neumann there—many mathematicians fleeing conditions in Germany and the East passed through Cambridge on their way to settling elsewhere. And it was Max Newman, who was lecturing on topology—the study of relationships between geometric spaces as they are transformed by such operations as stretching, but not such operations as cutting—who introduced him to the Hilbert problem that would make his career. Working on the Hilbert problem was not his first attempt at a dissertation—one professor had suggested he work on the dielectric constant of water, but he got nowhere.
David Hilbert’s Entscheidungsproblem (one of twenty-three famous Hilbert problems) had been proposed by the German mathematician in 1928. In layman’s terms, the Entscheidungsproblem asked if there was or could be a procedure (an algorithm) that could determine whether a mathematical statement was true or false—just the sort of question that no longer interested Atanasoff. To many mathematicians of the period, the Entscheidungsproblem seemed to point toward concepts that were psychological, epistemological, or even theological. Alan Turing’s answer to the problem was no—there was no algorithm that could determine the truth of every mathematical statement. He was preempted by a few weeks by American mathematician Alonzo Church, who was at Princeton. Church’s answer to the question was a logical system called lambda calculus. Turing’s answer was a different sort of act of imagination, and he came to it in a manner similar to Atanasoff’s revelation—he set out on a cross-country run along the river Cam. He was an avid and fit runner who occasionally ran north as far as Ely, some twenty miles from Cambridge. One day, resting in a meadow after a long run, he imagined a procedure, or set of instructions, so simple that a machine could perform it, if the machine could operate eternally.
In the paper he wrote about this idea, Turing describes the psychological process of making a simple but arduous calculation. He imagines that the person making the calculation is given a set of instructions, and if she follows the set of instructions every time she sits down to her work, her mind will always work in the same way, and she will make no mistakes in her calculation (though the work, of course, will be unbelievably tedious). Turing soon makes the leap from the set of instructions to the notion of an ideal machine—it would operate on its own, without human input. It would perform a set of operations forever, and the operations would be clearly defined and of a limited number. As his example, he described a machine that is fed an infinitely long tape. The tape is divided into squares, and each square either has a mark on it or is blank. As the machine scans each marked square or each empty square, it is instructed to perform an operation—to put a mark in an empty square, to erase a mark in a marked square, to shift one space to the right, or to shift one space to the left. When each operation is completed and the machine has moved on to the next instruction, it now scans the new square and performs the instruction for that square. However, the machine does not treat every mark and every blank in exactly the same way—the set of instructions progresses as the calculation progresses. This progression Turing called “the table of behavior.” We would call it the program. Eventually, the machine arrives at the end of the calculation—for example, it is instructed by the table of behavior to stop after erasing a mark and shifting to the left. This operation denotes that the answer has been arrived at—in the case of an addition problem, the series of marked squares now adds up to the sum of the marked squares defined by the problem.
Turing imagined all sorts of machines set up to solve all sorts of mathematical problems, including those considered impossible to solve. The only things necessary for these solutions would be instructions and time (and a binary number system consisting of marks and blanks). What would define a problem as soluble would be that the machine would progress to the end of the problem. What would define the problem as insoluble would be that the machine would get stuck—a wrong instruction sequence could set up the operation of the machine so that it would simply move back and forth, erasing and re-marking the same two squares. Turing then went on to imagine a comprehensive machine, which he called a “universal machine,” that, given sufficient instructions, could solve every problem that each of the specialized machines could solve. He showed that, given infinite time and instructions, there could be such a machine. The kicker, though, and in this he addressed the Entscheidungsproblem, was that by thinking through how his machine would operate to solve a problem, any problem, he could easily see the way in which a problem could be given to the machine that would stop the operations of the machine—that is, cause it to infinitely repeat an operation without arriving at a solution. And the only way to determine which problems would result in failure and which problems would result in solution was to try to solve them. Mathematics could not devise methods in advance that could predict the solubility of every problem, therefore the truth of a given statement could not necessarily be determined. In addition to this, while the machine could operate eternally, there was no way for the machine to check itself, and so there was no way to know whether every answer was “true” or not.
The lambda calculus “represented an elegant and powerful symbolism for mathematical processes of abstraction and variation,” but the Turing machine was a thought experiment that posited a mechanical operation, to be done by either a mechanism or by a human mind. Andrew Hodges, Turing’s biographer, points out that Turing’s idea “was not only a matter of abstract mathematics, not only a play of symbols, for it involved thinking about what people did in the physical world … His machines—soon to be called Turing Machines—offered a bridge, a connection between abstract symbols and the physical world. Indeed, his imagery was, for Cambridge, almost shockingly industrial.”
In May 1936, Alan Turing submitted his paper, entitled “On Computable Numbers, with an Application to the Entscheidungsproblem,” to the Proceedings of the London Mathematical Society and then applied unsuccessfully for a Procter Fellowship at Princeton. As far as anyone in England knew, only Turing and the American Alonzo Church had come up with answers to the Entscheidungsproblem. No mathematician in England was equipped to referee either Turing’s or Church’s paper.
Atanasoff and Turing, in their different ways, understood that counting was the future of computing, but the differences between them could not have been more clear—Atanasoff had to invent an actual, physical machine that when turned on would perform a useful function. Turing was imagining a process that was repetitive and mechanical, but since he himself was not an adept tinkerer, and he had never been asked to develop whatever engineering abilities he may have inherited from his family, his machine was meant to inspire invention rather than to be an invention. But the third early inventor of the computer, Konrad Zuse, did not think like either Atanasoff or Turing.