The Man Who Invented the Computer Part 4

When he called again to set up an appointment for bringing the Sperry lawyer, a man named Lawrence B. Dodds, to Maryland, Mauchly and Atanasoff chatted rather cordially. Mauchly explained to Atanasoff that Dodds was representing Sperry Rand in a case against Control Data and Honeywell, thus revealing to Atanasoff that neither he nor Dodds knew of Atanasoff's central position in the case Honeywell and Control Data were preparing. Mauchly's att.i.tude indicated that he had no idea that Atanasoff might be his antagonist in the patent dispute. His immediate reason for calling Atanasoff was that he had been subpoenaed in the patent dispute and had discovered old letters to Atanasoff that he had forgotten in the course of twenty-six years. He had also given a deposition. By this time, Atanasoff had read Mauchly's deposition, but he didn't reveal this, just suggested that he would try to get hold of it. In his deposition, Mauchly told Atanasoff, he had said a few things that might make Atanasoff "mad," for example "that when you got into administrative work you lost interest in computers." Atanasoff said, "Maybe I did seem to." Mauchly was surprised that Jean Berry appeared on the list of witnesses, but not Clifford Berry. Then Mauchly speculated that Berry had died recently, since he had seen Berry's letter to R. K. Richards describing the ABC and stating that only Mauchly had seen the ABC "in full." Hadn't Caldwell seen it? suggested Mauchly, referring to Samuel Caldwell of MIT, who had been asked to make an evaluation of the ABC for grant purposes. Atanasoff told him that no, Caldwell had never had the same detailed access that Mauchly had had. Mauchly then complained about Allen Kirkpatrick, the lawyer who had deposed him, who, he thought, "had practically accused me of plagiarizing everything I've done."

Mauchly arrived for his visit on the morning of December 16, 1967. Dodds appeared an hour later. Mauchly's manner revealed that he still did not understand Atanasoff's position in the case, and Atanasoff remained reticent. When Dodds arrived, Atanasoff was straightforward about what information he would give the Sperry lawyer-he would speak generally, but not specifically, about his deposition, and his position on Mauchly's visit would be clear. "Dr. Mauchly came to Ames on approximately June 15, 1941. He spent considerable time with the machine; he understood it fully, and in substantially every detail. If you don't like it, that is just too bad, because those were the facts."

Mauchly observed, "You are taking a very positive posture which I cannot take. Your memory is better than mine."

Gradually in the course of their conversation, it seemed to dawn on Dodds and Mauchly that Atanasoff was not as uninformed about the case as they had thought he was. Finally there was a revealing exchange: Mauchly: "Do you contend that I read the book?" (meaning the thirty-five-page description of the ABC) Atanasoff (after hemming and hawing): "However, the answer is yes, and you also asked me if you could take a copy home with you. I denied the request, and so you did not take the copy away."

Dodds: "Will you treat us as well as our opponents?"

Atanasoff: "I do not see why I should place you and your opponents on the same footing. It is obviously to your advantage to prove that there was no development of a computing machine at Ames, Iowa. Your opponents contend the contrary and my interests must lie in that direction."

Dodds then asked if anyone else "now alive" had read the ma.n.u.script and Atanasoff pointed out that it had gone to various agencies in hopes of funding. Then Atanasoff remarked that he had read the 827 patent that summer-"The 827 patent almost exactly described my own apparatus and its specifications." Then Mauchly had to be shown the 827 patent (which Atanasoff had a copy of), since he did not remember which one it was. Dodds and Atanasoff sparred a bit about the language of the 827 patent, Dodds saying that the patent didn't mention "regenerative memory" and Atanasoff pointing out that what was described-"interaction of logic circuits in the computing elements"-was his idea. Dodds acknowledged that this was so. Mauchly kept quiet.

Alice served lunch. As they got up to go to the table, Atanasoff remarked that the Honeywell/CDC lawyer had encouraged him to find every doc.u.ment and potential witness and remember every detail. Mauchly replied, "Our lawyers don't want me to remember anything."

Sometime later, Atanasoff could not help exclaiming, "Mr. Dodds, in the face of the facts, how do you expect to win this case?"

Dodds, irritated, replied, "You don't know anything about how federal judges are likely to act. They may decide the question upon their own impulse instead of fact, law, or reason." Mauchly and Dodds, it seems, could not help revealing themselves to Atanasoff. Atanasoff, on the other hand, did not reveal that Mauchly and Dodds's a.s.sumption that there had been no witnesses to Mauchly's work on the computer was wrong. Throughout the interview, Mauchly retained his strange presumption that he and Atanasoff were on the same side. Once Dodds left, Mauchly even remarked that Sperry was paying him a healthy consulting fee for his work on the case and suggested that Atanasoff might try to get the same sort of arrangement, and then he reiterated what he had said before, that the Sperry lawyers had advised him to remember his Ames trip as vaguely as possible. Throughout the rest of the afternoon (Mauchly was not inclined to depart), Mauchly continued to reveal details of the case, things he had seen, bits of advice he had received, royalties he had gotten for the patents, how he had gotten them, what he had done with the money. He showed a friendly interest in Atanasoff's own career (and evident prosperity), and Atanasoff was left with the feeling "that Dr. Mauchly was genuinely pleased to find that he had not entirely deprived me of living substance."

Atanasoff did not at all share Mauchly's casual att.i.tude toward the suit-like Jean Berry, he had become convinced that there had been foul play in Clifford Berry's death, and he even persuaded the Honeywell/ CDC lawyers to send a lawyer along with him back up to New York to look into the case. As usual, Atanasoff devoted himself to finding out everything he could, to thinking it through, and to persuading those in charge to see things his way. He did, in fact, talk to the detective in charge of investigating the case into reopening it-he did not think the levels of alcohol and medicines in Berry's blood (they were low) and the way that he had died (quietly, his arms at his sides) added up to a realistic case for suffocation by plastic bag. He was convincing enough for the immediate investigator, but not enough for his superior, and the case was not reopened. Atanasoff remained uncertain, at least publicly, about the cause of Berry's death-in subsequent interviews, it was clear that he could see both sides of the issue. Jean Berry was always certain that her husband had been murdered-he was the person who had the clearest information both about what the ABC was and how it worked, and how much time Mauchly had spent with the machine, what he had done, and what Berry himself had told him.

Each of the Honeywell/CDC witnesses had something different to offer: Sam Legvold had seen Mauchly around the computer in the bas.e.m.e.nt of the physics building; Lura Atanasoff had seen him in her home, with the copy of the description of the ABC in his hands, and pens, and bond paper, with his light on late into the night; R. K. Richards had Berry's clearly stated correspondence on the issues under question. And then, Atanasoff offered to have several technicians in his Maryland machine shop take the thirty-five-page written description of the machine and build a complete demonstration model. Alice Atanasoff went shopping for the exact outmoded parts that they would need (though the proper 1940-vintage vacuum tubes were hard to find). It was agreed that Atanasoff himself would neither oversee the construction nor partic.i.p.ate, just to demonstrate that the description was enough of a blueprint. When it was built, in the summer of 1968, it worked beautifully and did everything Atanasoff said it would. Atanasoff himself was so pleased with it that he built another one for himself.

Data gathering and record gathering continued through 1968, with the Honeywell lawyers and the CDC lawyers seeking out every doc.u.ment and witness. The Sperry lawyers were not as industrious, and neither was Mauchly-when he appeared for discovery in October 1968, he had only a few papers with him, all, he said, that he could come up with. The Honeywell/CDC lawyers had to remind him that he was legally bound to search out everything that he could find. They questioned him for three days, most particularly about three separate issues-what were the precise concepts he had thought up on his own before his December 1940 discussion with Atanasoff at the annual meeting of the American a.s.sociation for the Advancement of Science, what had he done and learned in his June trip to Ames, and what had he intended to say in his correspondence with Atanasoff after his visit. Mauchly could hardly remember anything, and he remarked over and over that he had a bad memory. The lawyers could not tell whether he actually could not remember anything or whether he was following instructions from Sperry lawyers. He repeated that he had not used any of Atanasoff's ideas and that the ABC was "an incomplete machine" and "would not do" what it was intended to do. At least that much he remembered. He did not seem to realize that he was contradicting himself.

Atanasoff's deposition, which began eleven days after Mauchly was finished, was the exact opposite of Mauchly's in many ways-he had plenty of evidence that he had thought about and tried out various concepts before and after his revelation of December 1937, including grant proposals. He also had a clear memory of his own thinking, and of events surrounding Mauchly's visit (a memory that was corroborated by his witnesses). He was so organized that the lawyers could suggest only very small ways to shape his testimony to make it more forceful or more clear-he had an excellent grasp not only of what he had done with the ABC, but also of what he was doing in the case.

When Mauchly returned for a second session of questioning in April 1968, he brought a large stash of doc.u.ments that he had managed to uncover. Unfortunately, they had the effect of supporting Atanasoff's contentions, not his own-whether or not Mauchly now remembered that the ABC worked, he had written enthusiastically to friends in 1941 that the computer could "perform all kinds of mathematical feats." Charles Call read the doc.u.ments while another lawyer deposed Mauchly. Call then told the other lawyer what he found in the doc.u.ments, and, using this information, the other lawyer challenged Mauchly's testimony. Mauchly thereupon modified his testimony. As his own biographer remarks, "He made a huge mistake by obfuscating the facts of his Iowa visit." In ENIAC, McCartney tries to make a case for Mauchly having had ideas about a computing device before he went to Ames-according to a colleague, he invented a "little computing device ... [that] used neon tubes as trigger circuits. And he'd done some simple arithmetic work on the desk setup, using those triggers." But this is a defense of Mauchly that Mauchly did not make for himself, possibly because, according to Mollenhoff, his device was a single neon tube mounted on the lid of a Quaker Oats box that turned on and off.

In some ways, John Mauchly remains the most mysterious and contradictory figure of all of our computer innovators. There is no evidence that he was coldly calculating in any sense of the word. His efforts in every direction seem to have been expansive, impulsive, and inclusive rather than cool and directed. When J. Presper Eckert's second wife remarked that Mauchly could not have put together ENIAC without Eckert, but that Eckert would not have thought of it without Mauchly, she was portraying Mauchly as a certain type of genius-a disorganized dreamer full of inspiration that comes from nowhere. However, everyone, including those who knew him through Atanasoff, remarked on his sociable nature and his apt.i.tude for conversation, and so the evidence is that his ideas did come from somewhere-from others, if only in embryonic form. This, too, accords with certain theories of creativity (most particularly those delineated by Malcolm Gladwell in Outliers)- that "genius" is a social phenomenon, that ideas grow out of human intercourse, that certain communities produce a wealth of talent because of certain mores of interaction. One such habit, Kati Marton would say, was the way Jews in Budapest of the 1920s loved to linger in cafes, smoking and talking-perhaps the world in which John von Neumann came to believe that some ideas should not be possessed and patented by individuals. Mauchly was a connector extraordinaire-every story about him attests to that; in each description of him, even when he begins by a.s.serting something (for example that he remembers nothing of a particular event) he soon comes round to remembering it much in the way his interlocutor does. As Atanasoff discovered in December 1940, Mauchly was by nature an enthusiast, and in 1941, when his colleagues at Iowa State were skeptical of his computer, the very person Atanasoff needed to support his own confidence in his machine was an enthusiast who seemed at least somewhat knowledgeable.

Atanasoff seems not at all like Mauchly-he was well organized and well directed above all things. As a "problem finder," he had a special talent for formulating specific questions that required solution-as at Bikini Atoll, for example-and then using available materials to come up with the best available solution, if not necessarily the ideal one. But like Mauchly, his talents thrived on social interaction-as he taught his students, he learned from them; as he directed their work, he came up with ideas for his own. His quest for the computer grew out of his understanding of a general need belonging to his community of mathematicians, physicists, and engineers. He was stimulated by everything from the slide rule he got from his father as a boy to methods of house construction he employed in retirement. What had already been discovered and invented served Atanasoff as a springboard to other things. At the same time, he was good at progressing from level to level-at learning from Charles Babbage's unfortunate experience not to try to invent the universal machine before you have gotten the specific one to work. Atanasoff was Mauchly and Eckert rolled into one-he had grand mathematical ideas and he had specific engineering ideas. He understood what both kinds meant and he understood how the two fit together. And then he was blessed with a perfectly congenial partner, Clifford Berry, whose building process was smooth, thoughtful, and efficient. Like Atanasoff, it did not occur to Berry to try a zillion things at once or to drop one project and begin another before the first was completed.

Sperry had one advantage at the trial, the considerable one of the reluctance of courts to overturn patents already granted. But Honeywell and CDC had one, too-Mauchly was required to prove a negative, to prove that he had not been influenced by the time he had spent in Ames, and to prove that he was neither lying about his memories nor simply failing to remember things that he had thought and done. McCartney maintains that the case "boiled down to one scientist's words against the other," but in fact many of the words the Honeywell and CDC lawyers were using against Mauchly were his own. And the Honeywell lawyers went about their case in an Atanasoffish way-exhaustively. They put all their doc.u.ments together in electronic legal files, which gave them excellent organization and ready access. They seemed to realize, as the Sperry lawyers did not, just how useful computers could be.

The Honeywell and CDC lawyers also understood that they had to supply expert witnesses for the trial who could explain to the judge, Earl R. Larson, what the issues at stake were-how computers worked, how the ideas in the ABC were linked to ENIAC. Larson had an excellent reputation as a scrupulous judge whose opinions were rarely appealed and even more rarely overturned. He intended to preserve this reputation in what he soon came to understand was one of the most important intellectual property cases of the twentieth century. He knew that he had plenty to learn and that he had to take the time to learn it. The Honeywell/CDC lawyers hired Isaac Auerbach a.s.sociates (the same Isaac Auerbach who had asked Mauchly at the panel Call witnessed about his visit to Iowa State), and Auerbach supplied him with three computer experts who had worked on both ENIAC and EDVAC. The witnesses had several jobs: corroborating and explaining Atanasoff's testimony to the judge; informing the judge of the relevant history of the computer; reading and explaining the thirty-five-page report on the ABC; corroborating that the model newly constructed from the old plans was as it was said to be; and ultimately tracing connections from ABC to ENIAC and EDVAC.

The trial in Minneapolis began on June 1, 1971.

The question of whether the ABC had existed and the question of whether Mauchly pirated Atanasoff's ideas for ENIAC were separate though related. What Mauchly and Eckert had fallen prey to with von Neumann and Goldstine's 101-page publication of the ideas that led to EDVAC was a question of prior art-in typing up and sending out under von Neumann's name the ideas underlying EDVAC, Goldstine established them as prior art to any claims that Mauchly and Eckert might make to the same ideas (von Neumann's biographer, Norman Macrae, sees this as von Neumann's intentional attempt to preempt the patenting of the ideas underlying the computer). If Atanasoff's thirty-five-page description of the ABC had had the same sort of distribution as von Neumann's paper (at least two hundred copies), then it would have stood as prior art. But Atanasoff had made only five copies on the a.s.sumption that because Iowa State was planning to patent the machine, it was dangerous to make more copies.

Much of the case, especially Atanasoff's testimony, revolved around the question of what ideas he had come up with and how he had come up with them. Because of this, the first part of his testimony was autobiographical-Attorney Henry Halladay questioned him about his childhood and his education in a detailed manner intended to delineate the steps by which he came to a set of concepts so unusual and innovative that other geniuses had not been able to come up with them, including Mauchly. Atanasoff obliged-yes, his fascination with his father's slide rule had driven all other, more common pa.s.sions like baseball out of his mind; yes, he had read his father's books on engineering and his mother's books on algebra, not because he was required to, but because he enjoyed them. His education at the University of Florida and the University of Wisconsin and Iowa State showed that he was a more-than-exemplary student (and chimed nicely with Judge Larson's own career at another land-grant university, the University of Minnesota).

Atanasoff was not the first to testify-Sam Legvold and others set the stage, so when Halladay brought Atanasoff's testimony around to the subject of his years at Iowa State, it was easy to see that his teaching career in the thirties, and the evidence of not only his own work, but also the work of his students (one piece of evidence was the t.i.tles of papers his students had written under his tutelage) showed that he had thought through computing ideas for a long time and in more than one way. This history prepared the way for Atanasoff's clearly remembered and detailed recollection of that night in the Rock Island tavern in December 1937.

Halladay pressed him on two ideas, regenerative memory and logic circuits. Of the first he said, "I'm thinking about the condensers for memory units, and about the fact that the condensers would regenerate their own state so their state would not change with time. If they were in a plus state, for instance, they would stay in a plus state; or if they were in the negative state, they would stay in the negative state. They would not blink off to zero. Or if you used two positive charges, they would retain their individual ident.i.ty and would not leak across to one another."

Concerning logic circuits, Atanasoff was honest about the fact that he did not perfectly visualize how the logic circuits would work. He imagined a black box, with input from two memory units-"the box would then yield the correct results on output terminals." Although he did not envision the contents of the box specifically, he did understand that "since I was going to use condensers, why then I supposed the innards would be electrical in character, and I was well aware that the electrical ent.i.ties which would be as suitable for such a purpose were vacuum tubes." He explained that "condenser" was an archaic term for "capacitor." Atanasoff then described how for the next fifteen months, he worked out these two ideas on paper: the idea for the regenerative memory was fairly simple; what was to be in the black box was much more difficult, but he worked that out for both a binary number system and a decimal number system. When he compared the two, it was evident that the decimal system would be too unwieldy. He declared that he had clarified his ideas by March 24, 1939, when he submitted his two-page grant application, asking for funds. Although the letter was short, it was detailed, describing the three sorts of problems Atanasoff expected his calculator to be able to solve (electrical circuit a.n.a.lysis, approximate solution of differential equations, and multiple correlation). His machine would be able to solve these sorts of problems for many more variables than was then practical with mechanical calculators. The letter also described previous efforts he had made to solve these sorts of problems using already invented methods. He asked for and was granted $650 (some $7,800 in 2010 funds). All of his papers were in order and were presented to the court.

On the second day of testimony, more papers were presented. In fact, so many papers were presented-letters, notes, papers, diagrams, drawings-that Atanasoff began to weary of the tedium of court procedure, which meant putting descriptions of every piece of evidence introduced into the record. He was pleased, however, with the Des Moines Tribune article from January 15, 1941 (see this page). The importance of the article for the case was clear-the ABC was not a piece of junk that barely functioned, as Mauchly had gotten in the habit of saying.

The next item on the agenda was Atanasoff's version of Mauchly's visit. He was equally detailed. Mauchly had arrived on Friday evening. Over the weekend, they had visited the computer several times and talked about it constantly-with only one small break, during which they spoke of Mauchly's interest in meteorology. Mauchly had carried around the green-covered thirty-five-page description of the computer. Atanasoff had seen him reading it, and he and Atanasoff had discussed some of the things in the booklet that Mauchly wanted to understand. Atanasoff had explained the binary number system to Mauchly, though he was unsure how clearly the Philadelphian had grasped it. To Atanasoff, Mauchly had seemed eager to understand the ABC: "He seemed to follow in detail our explanations and expressed joy at the results, at the fact that these vacuum tubes would actually compute. He was shown addition and subtraction and multiplication and he was also shown the process of punching cards but we only had one unit in operation during his visit and we weren't prepared to punch all of the thirty 'Abaci' simultaneously and no effort was made to fill the entire machine. He was shown the operation of converting base-ten cards to base-two numbers on the system, then the rest of the controls which we planned for the machine to make it operable in regard to solutions of simultaneous linear equations ... We discussed logic elements in considerable length with Dr. Mauchly." Halladay also introduced as evidence a letter Mauchly had written to a friend on June 28, 1941, only a few days after returning to Philadelphia. The third paragraph included the following: "Immediately after commencement here, I went out to Iowa State University to see the computing device which a friend of mine is constructing there. His machine, now nearing completion, is electronic in operation, and will solve within a very few minutes any system of linear equations involving no more than thirty variables. It can be adapted to do the job of the Bush Differential a.n.a.lyzer more rapidly than the Bush machine does, and it costs a lot less." The Sperry lawyer tried to get this letter excluded on the grounds that it was hearsay, but the judge allowed it.

Even though the court procedures were tedious, Atanasoff's answers were so detailed and self-reinforcing, since he rarely contradicted himself or seemed confused, that when the Sperry lawyer cross-examined, both on technical issues and concerning his relations with John Mauchly, he succeeded only in bolstering Honeywell's case by giving Atanasoff the opportunity of adding more to the record. At one point, the lawyer a.s.serted that Atanasoff had referred to Eckert as "a high-powered electronics expert." Atanasoff coolly denied this and said that he had no knowledge of Eckert's skills. The lawyer asked him why he hadn't progressed with the naval computer when he was at the NOL. Ignorant of von Neumann's funding machinations, Atanasoff replied that he had been short of both personnel and time-the navy had promised to relieve him of his ordnance responsibilities but had failed to do so. His reply made perfect sense.

When Atanasoff was finished testifying-seven days of direct examination and three days of cross-examination-he had made the best case he could that Mauchly had not only visited the ABC, but he had given every evidence of understanding the principles underlying Atanasoff's theory of computing, as well as how he had realized these ideas in a piece of machinery.

One of the star witnesses for Honeywell, who testified at the end of August, was Edward Teller. His job was not to say where he thought Mauchly had gotten his ideas, but to help Honeywell's prior-use case against the ENIAC patents. According to Teller, the scientists at Los Alamos, thanks to the von Neumann connection, had made use of ENIAC for calculations concerning the feasibility of the hydrogen bomb in late 1945 and early 1946. The calculations were not especially accurate, but accurate enough to show Teller where he was in error and to suggest which direction he might go in when development of the H-bomb was resumed in 1949. The use of ENIAC for these calculations, and their significance as prior use, had not been employed in the previous trial that resulted in Sperry being awarded its patent. Its significance was in the fact that Mauchly and Eckert had not bothered to write up their patent application until August 1947, two and a half years after the machine was employed for the H-bomb calculations. It was a similar argument to the one that had been made about the EDVAC patents after the dissemination of von Neumann's 101-page "First Draft." Prior use was the second string to Honeywell's bow.

John Mauchly did not testify until November 1971. The Sperry lawyers had already discovered that Mauchly's depositions were easily challenged: such a.s.sertions as the one that he had spent only an hour and a half with the computer, or that he had not seen it running, or that he had not seen it with the cover off were so easily disproved that Mauchly's story had changed from deposition to deposition. The Honeywell lawyers knew how to press him because he had already given them plenty of ammunition.

However, the Sperry lawyers did what they could to establish Mauchly's credentials-like Atanasoff, he told his life story. Like Atanasoff, he outlined what he had done before ENIAC that might have pointed to his computer ideas. Then Halladay cross-examined him. Judge Larson had prohibited witnesses from hearing the testimony of earlier witnesses, so Mauchly did not know what Legvold, Atanasoff, Lura Atanasoff, and others had said about his visit (though he had read their depositions). Throughout his testimony, he persisted in denigrating the ABC and forgetting what was in the thirty-five-page description of the machine. Then Halladay began to cross-examine him, and Mauchly's inability to remember fairly elementary aspects of his earlier inventions (such as whether his Harmonic a.n.a.lyzer was mechanical or electronic) worked against him. He could not come up with any drawings or ideas he had made prior to meeting Atanasoff. He could call no witnesses who remembered talking to him about such devices, and he could not point to having invented a digital device-his Harmonic a.n.a.lyzer was a.n.a.log. He talked about having discussed electronic computing in his cla.s.ses at Ursinus but could recall no student who could attest to these discussions. The only papers or notes he had about electronic computing were dated after he met Atanasoff in December 1940 or after he had been to Ames.

One of the most striking pieces of evidence that Halladay introduced was a paper Mauchly had written in August 1941, two months after seeing the ABC, in which Mauchly had stated "computing machines may be conveniently cla.s.sified as either a.n.a.log or impulse types," appending a footnote that read, "I am indebted to Dr J. V. Atanasoff of Iowa State College for the cla.s.sification and terminology here explained."

At one point, Halladay showed Mauchly the thirty-five-page report, which the Ames people remembered him studying. Mauchly said that he had not read it very carefully, because he was not interested in the machine it described. Halladay pushed him, and he became resentful but finally admitted, in a roundabout way, that Atanasoff had told him that he could not take it back to Philadelphia, and so he must have asked to do so. Throughout the cross-examination, Mauchly quibbled and resisted, but Halladay did eventually establish several points-that after the twenty- to thirty-minute December meeting in Philadelphia, Mauchly had understood that Atanasoff was building a calculator based on different principles from the Bush a.n.a.lyzer and that if he came to Ames, he could see it and Atanasoff would tell him about it. Concerning the June visit, Halladay established that Mauchly had been there for five days, that he had discussed the computer for many hours with both Atanasoff and Berry, that he had seen the ABC operate and read the report, that he had expressed enthusiasm for and understanding of the ABC and Atanasoff's ideas after returning to Philadelphia, and that he had asked Atanasoff if he could use some of his ideas in a calculator of his own. It was also established that after he got back to Philadelphia, he had changed his career path and enrolled in the summer course in computing theory, where he met Eckert.

In Mauchly's defense, Scott McCartney reports that at the time of the trial, Mauchly was suffering from an illness that damaged his memory. I think we can also infer that Mauchly looked back at the ABC through the lens of ENIAC. There is no disagreement that ENIAC was a more complex and powerful computer than the ABC, and that it also owed some of its design and construction to the Bush a.n.a.lyzer at the Moore School that had been designed by Irven Travis before he left for the navy. ENIAC was intended to perform a war-related function and had to be put together as quickly as possible, which was why EDVAC was designed-to finally realize the most advanced computing concepts without the pressures of speed or limited funding. There is also no disagreement that J. Presper Eckert and the others who worked on ENIAC contributed to the development of a sophisticated machine that was in some ways advanced (and in some ways not) compared to the ABC. What the Honeywell lawyers endeavored to show was a "sine qua non" or "without which not"-that without Atanasoff, Berry, and the ABC, Mauchly could not himself have come up with the ideas that led to ENIAC. Nothing Mauchly could or could not remember proved that he could have, whereas all of the Honeywell/CDC evidence showed that Atanasoff had done so.

Mauchly might have had better luck in another country. Because he had to file his patent applications in the United States, he had to deal with a "first-to-invent" system (as opposed to a "first-to-file" system). In the U.S. system, invention is seen as both conception and "reduction to practice"-that is, more or less, making something. In order to get a patent, an inventor can't just think something up, and he also can't just make something-he must do both. Once the invention is made (or put into practice), however, the date of the invention is considered to be the date of conception rather than the date of filing. As a result, a patent application filed later can supersede one filed earlier if the inventor can prove both conception and diligence. It was pretty clear from the testimony that Atanasoff had been diligent in conceiving the computer and in "reducing it to practice." But the United States is the only country that uses such a standard. In any other country in the world, Atanasoff would have entirely lost his chance to claim the ideas behind the computer when Iowa State and Richard Trexler failed to file his application, and Mauchly would have been awarded the patent.

In this regard, it is also important to note that Mauchly could have avoided patent problems if he had been more careful, as GE lawyer George Eltgroth understood. If he and his lawyers had submitted material acknowledging and doc.u.menting what he had learned from Atanasoff in June 1941, as they were required to do, the patent examiner would have considered his claims in light of that material and determined if Atanasoff's machine (and his thirty-five-page report) qualified as prior art. The fact that he did not do so left him open to having the patent abrogated for what is called inequitable conduct. But Mauchly and Eckert, possibly hyperaware of the commercial possibilities of the computer (for which McCartney, a writer for the Wall Street Journal, specially praises them) were loath to give any credit to others-when they filed their patent, it covered more than a hundred different concepts, even though they were part of a large group working on the machine and Mauchly was also consulting Atanasoff from time to time on technical details of the ABC. It may be that when von Neumann was himself chatting up Atanasoff at the NOL, in late 1945, he was not only getting the benefit of Atanasoff's ideas, he was also coming to understand that the computer as it existed in 1945 could not be owned by one or two men and was figuring out how to make sure that it would not be. It may also be that it was von Neumann's insufficient credit to Mauchly and Eckert in his "First Draft" that put them in a possessive frame of mind when they were writing up their own application.

At any rate, the Sperry Rand defense of having Mauchly forget as much as possible was the best the Sperry lawyers could come up with. It was certainly one that was congenial to Mauchly, however well it was or was not designed to work, and he stuck to it. Another irony of the case, which Charles Call communicated to Kirwan c.o.x, was that if Sperry had offered to share the patents for the same fee as they asked from IBM ($10 million), Honeywell would not have gone to court; but Sperry asked for $250 million before the publication of R. K. Richards's book, and then $20 million afterward. Twenty million dollars was still too high for Honeywell, and so they went to court.

The challenge to Sperry Rand's patents was lengthy and involved. According to Clark Mollenhoff, it "consumed over 135 days or parts of days." A total of seventy-seven witnesses had given oral testimony, and an additional eighty witnesses were presented through deposition transcripts. Honeywell had introduced 25,686 exhibits to be marked by the court; and lawyers for Sperry Rand and its subsidiary, Illinois Scientific Development (ISD), had directed the court's attention to another 6,968 exhibits ... The highly complicated trial transcripts stretched to over 20,667 pages." Honeywell's brief, filed in September 1972, was five hundred pages long. The key claim in the brief was not that Atanasoff had invented ENIAC, but "that there is no difference between what Mauchly learned from Atanasoff in June 1941, and what Eckert and Mauchly were later to claim to have invented alone." The Honeywell brief went on to point out that even if the ABC had not worked, under U.S. patent law "one cannot claim a conception derived from another as his 'original' invention, even though he may have built the first device based upon that conception." The Sperry brief, filed in August, rested its case on the fact that Sperry had already been awarded the ENIAC patents and that Atanasoff had not invented ENIAC, and that Mauchly had done a few electronic projects before meeting Atanasoff.

In April 1973, Judge Larson sent copies of his proposed decision to both the Sperry lawyers and the Honeywell lawyers, asking for their responses. It was clear from the proposed decision that Larson was leaning toward abrogating the Sperry patents, but also that he was giving the Sperry lawyers one last chance to make their case. They could not make it. In October, Larson decided in favor of Honeywell, in no uncertain terms. He stated, "Between 1937 and 1942, Atanasoff, then a professor of physics and mathematics at Iowa State College, Ames, Iowa, developed and built an automatic electronic digital computer for solving large systems of simultaneous linear equations." He then went on to describe the steps by which Atanasoff solidified this claim-for example, it was enough that the breadboard prototype worked and was the subject of further funding. The ABC did not have to work perfectly at the time of Mauchly's visit in order to have established that Atanasoff's ideas were valid, that they were his ideas, and that he communicated them to Mauchly sufficiently so that Mauchly could build on them. Larson stated that "as a result of this visit, the discussions of Mauchly with Atanasoff and Berry, the demonstrations, and the review of the ma.n.u.script, Mauchly derived from ABC 'the invention of the automatic electronic digital computer' claimed in the ENIAC patent."

Larson also addressed the issue of who had invented ENIAC. He found that "work on the ENIAC was a group or team effort and that inventive contributions were made by Sharpless, Burks, Shaw, and others," but that since these people had not a.s.serted their claims in a proper manner, Honeywell could not use these claims to abrogate the patents.

On the same day that Judge Larson gave his decision, Archibald c.o.x was fired as special Watergate prosecutor, and Larson's decision was lost in the news shuffle of Watergate. But in spite of the wishes of those involved, the decision was in fact a technical matter, of interest to computer geeks and corporate lawyers, not the public at large. Computers themselves were still seen as room-sized, specialized pieces of machinery, not accessible to the average person. The importance of Judge Larson's decision would not really be clear until the computer companies had acted on it. The result was as John von Neumann had suspected-once the ideas became common property, innovation blossomed, and the computer revolution took hold.

Chapter Twelve.

Sperry Rand, John Mauchly, and J. Presper Eckert did not go down easily. They took advantage of the limited dissemination of the Minneapolis decision to continue claiming credit for inventing the computer. Possibly they did not understand the details of patent law that destroyed their claim-from the beginning, they seem not to have seen themselves as team members or as the beneficiaries of social networks engaged in a common purpose, but rather as stars and owners who stood to gain fame and fortune. When they claimed owners.h.i.+p of more than a hundred ideas in their 1947 patent application, or when they failed to acknowledge Atanasoff in that same application, they were setting themselves up for an eventual failure that might have been avoided with smarter legal counsel, more scrupulous honesty, or, just possibly, better recordkeeping.

For years, Sperry Rand and Mauchly and Eckert fought a rearguard action to retain the PR rights to the invention, if not the legal rights. One patent lawyer, Sheldon L. Epstein, of Wilmette, Illinois, recalls how difficult it was to get any mention of Atanasoff or the Larson decision into a Smithsonian exhibition on the history of the computer: "In the 1980s, the Smithsonian Inst.i.tution started work on an exhibit to commemorate the invention of the computer. Because it lacked funds to proceed on its own, the Smithsonian solicited and received computer industry funding. One of the more prominent contributors was Sperry Rand. The Smithsonian Inst.i.tution took the position that contributions from Sperry Rand and other supporters of Mauchly and Eckert would not influence the content of its exhibit. Nevertheless, the exhibit as originally conceived did not contain any reference to Atanasoff's inventions or to Judge Larson's opinion. Instead the Smithsonian Inst.i.tution credited Eckert and Mauchly with invention of the electronic computer. Atanasoff's supporters strenuously objected and had some limited success in getting a very small portion of the exhibit allocated to Atanasoff's inventions. That same problem was to reappear a few years later when PBS produced a program-financed by many of the same contributors-on the invention of computers."

In 1999, Wall Street Journal writer Scott McCartney took up the cudgels again, this time in the interests of private enterprise. In ENIAC, McCartney maintains that it was Mauchly and Eckert who started their own company, and Mauchly and Eckert who foresaw the computer revolution as we know it. The idea of individual access to inexpensive and powerful machines that would be used for all sorts of things was unimaginable to people like John von Neumann, who thought that computers would be large tools for government agencies, academia, and giant corporations, but limited in their usefulness for the average person. Even though Mauchly and Eckert actually showed no apt.i.tude for private enterprise, McCartney views von Neumann as the real thief, with his attempts to spread the principles behind the computer to anyone who might be interested and thereby spark greater and more powerful inventions. For McCartney, Atanasoff and his claims are just an annoyance to be dispatched with a.s.sertions that the judge didn't know what he was doing and Sperry's lawyers didn't either. But Sperry never appealed the decision, and so they must have accepted it. One especially interesting response to McCartney's book demonstrates the resentment that lingered for a long time. At Amazon.com, in the reviews of ENIAC, JBartik writes: Scott struggles hard on the Atanasoff saga. Atanasoff never claimed he invented the computer and n.o.body ever heard of him until Honeywell dug him up to keep from paying royalties on the ENIAC patent. Much is made of John Mauchly's memory of his a.s.sociation with Atanasoff as recorded at different times. John suffered from a disease called Hereditary Hemoragic Talengetasin (HHT) [sic] which causes lesions to be formed in the brain and holes in the lungs. One of the interviews was taken shortly after he had had an episode and had been very ill in the hospital. It is no wonder he couldn't remember incidents then that he could remember when he was in better health.

"JBartik" turns out to be Jean Bartik, whom McCartney acknowledges at the end of his book: "Jean Bartik was a fountain of information and a burst of energy who spurred me on several times during research and writing." She is pictured in one of the famous photos of ENIAC (identified as Betty Jean Jennings). McCartney also declares that he owes a great deal to Mauchly's wife, Kathleen Mauchly Antonelli (a good friend of Bartik's) and to Eckert's wife, Judy. It is clear from these acknowledgments that what happened to ENIAC and EDVAC gave rise to bitter feelings on both sides of the patent issues. In the 1980s, Alice and Arthur Burks wrote a book supporting Atanasoff and demonstrating the links between the ABC and ENIAC-Arthur, of course, worked on ENIAC and the IAS computer. Alice worked on ENIAC with Jean Bartik. In 2003, Alice Burks returned to the fray with Who Invented the Computer? The customer reviews on Amazon.com give a sample of the pa.s.sions raised on either side by the dispute of the ENIAC patents.

But Atanasoff was not without his own advocates and promoters. While the trial preparation was going on, in 1970, Isaac Auerbach happened to meet a Bulgarian mathematician named Blagovest Sendov at a conference in London and to mention Atanasoff. Sendov was immediately interested and did some of his own checking into the case. He also wrote to Atanasoff, requesting information about his father, Ivan. Iva Purdy Atanasoff, then visiting John and Alice, put together her memories, and Sendov used this information to find Atanasoff's relatives in Bulgaria. Atanasoff was invited to return for a visit, and, while there in November 1970, he was awarded the Order of Cyril and Methodius, First Cla.s.s, for inventing the computer. He was also shown around the city of Sofia and taken to Boyadzhik and the Yambol district, where his father was still remembered.

When the Larson decision was handed down, Atanasoff was just seventy. He was still enormously active on his Maryland farm, busy with his wife, Alice, his three children, and his grandchildren. How busy is apparent from Tammara Burton's reprint of a letter written by Atanasoff's mother Iva (now almost a hundred) after she moved to the farm in the mid-1980s: "Vincent ... wants me to walk to the gate [about 850 yards] every day even when it is below freezing. Then I have this bell which rings every hour for me to get up and walk around." Iva comes to rather enjoy her freezing exercise, though one day when there is blowing snow, she persuades Alice to intercede with her son. As for Atanasoff himself, she reports, "One fourth of the time he spends lecturing me about the great necessity of eating less, drinking more, and walking more. The other three-fourths ... he spends in the machine shop. All we can hear is screech screech scrunch. I asked him what he was making and he said a boat. I supposed a small pleasure boat but wondered because he does not care for fis.h.i.+ng. But he said it would be about as big as a house."

Atanasoff's real pa.s.sion late in his life became language and alphabets. He viewed the Bulgarian version of the Cyrillic alphabet, with thirty-two letters until 1945 and thirty thereafter, as superior to the English alphabet, and when interested groups wanted him to talk about the invention of the computer, he wanted to steer the conversation toward the benefits of reinventing the alphabet (the reader may view this as an eerie evocation of Alan Turing and the purpose of Colossus). He told a Bulgarian newspaper in 1985, "I hear them; I hear the voices and the hearts of the people who p.r.o.nounce them ... I want each letter or each symbol to carry more meanings, to support with full power the alphabet."

Atanasoff gained more and more recognition for the invention of the computer as the twentieth century progressed (in spite of his omission from the MIT website). He was celebrated at Iowa State in 1974, and he was the subject of a meticulous biography that focused on the relations.h.i.+p between the ABC and ENIAC by Arthur Burks and Alice Rowe Burks, who had worked on ENIAC, in 1989, called The First Electronic Computer: The Atanasoff Story, as well as a biography called Atanasoff: Forgotten Father of the Computer, by Clark Mollenhoff, a writer for the Des Moines Register, in 1988. The Burkses, according to Tammara Burton, had been unaware of the ABC until they wrote an article for The Annals of the History of Computing about ENIAC. They read the transcripts from the trial and wrote, "Atanasoff's principles for electronic computation played a crucial role in the circuitry of ENIAC and all its successors." But the Burkses' book was published by the University of Michigan Press and the Mollenhoff book was published by Iowa State University Press. Burton's own excellent book, which contains more personal information about Atanasoff, was published in 2006 by the All Bulgarian Foundation and the Center for Research on the Bulgarians.

In 1990, Atanasoff went to the White House and received from George H. W. Bush the 1990 Medal of Technology "for his invention of the electronic digital computer and for contributions toward the development of a technically trained U.S. workforce." He was also nominated for the n.o.bel Prize in Physics three times during the 1980s, but, according to Burton, since his thirty-five-page paper describing the ABC and other papers concerning the theoretical and technical aspects of the ABC were never published, he was not eligible. Atanasoff died on June 15, 1995.

Many of the questions that McCartney and Bartik attempt to dismiss in ENIAC concerning the ABC were addressed in the 1990s, when a team of computer engineers and graduate students led by John Gustafson rebuilt the ABC, replicating as closely as possible the tools, materials, and construction methods that Atanasoff and Berry had used in the late 1930s. The building of the replica was informative in several ways, according to Gustafson. For one, "The ABC replica took three years to build, the same as it took Atanasoff and Berry. It was hard to get the parts, and a lot of the necessary skill sets don't exist anymore, such as putting together gear trains and synchronous electric motors. We needed people who were good old-fas.h.i.+oned electronics engineers. The replica cost about $600,000, about the same adjusted for inflation, as it cost when Atanasoff and Berry built it." And, contradicting a frequent a.s.sertion by ENIAC partisans, it did work. Gustafson says, "One of the reasons I built the replica was to see if it worked, and yes, it did work, but not on full size problems (ones with 29 variables)-it could do five equations and five unknowns. Beyond five, it would get messed up in the 'scratch result,' that is, writing down the output. [Atanasoff] had to invent a way of storing the intermediate results, and he invented electric arcs zapping holes into paper cards. You could sort of read it back, and it made a mistake in about 1 out of 100,000 holes, which seems like a lot, but in a binary system is not, really." Gustafson estimates that it would have taken him and his group two years to solve the scratch result (or charring) problem, the same amount of time it probably would have taken Atanasoff and Berry, because it was not only the nature of the card stock that was the difficulty, it was the size and capacity of the card stock-"The computer worked well up to five equations and five variables, but it was another step of difficulty to go from five to six-part of the difficulty rose from the setup of the IBM card, and part was owing to the setup of the switches. The theory of the computer was in terms of groups of five."

If we survey the history of the invention of the computer, the path by which the instrument on which I am typing came to exist, then we have to say that it was a peculiar and tortured path. Absolutely pivotal to the existence of the computer was the Second World War. From Atanasoff's point of view, without the Second World War, he would have been in Ames to make sure that his patent application was filed and, possibly, to make sure that the lawyer, Richard Trexler, understood it; he would have found the proper card stock for charring his results; his machine would not have been dismantled and hauled away. From Zuse's point of view, his machines would not have been bombed into smithereens; he would have filed his patents and secured proper component parts; he would have, perhaps, more easily benefited from the insights and aid of Helmut Schreyer, who might not have left Germany for South America; he would not have had to evacuate Z4 in the mountains where he was stranded for years; he would have had access to computer experts in other nations. From Tommy Flowers's point of view, he might have taken his vacuum-tube idea and used it to invent a computer, but he also might not have met Alan Turing or Max Newman; the computer he invented would not have been Colossus, but on the other hand, he would not have had to invent it and then destroy it within two years, never referring to it again for decades. From Turing's point of view, he might have had plenty of good ideas about how the mind works and what a computer would be like, but he would not have met Tommy Flowers and the other engineers who understood how to make something. From John Mauchly's point of view, he would not have had access to Herman Goldstine or the team of physicists, engineers, and operators that gathered together in Philadelphia to solve the problem of those firing tables, and the money they had access to. From John von Neumann's point of view, he would not have had his Los Alamos experience, which showed him both what a computer was needed for and how successful (but destructive) collaboration could be, and he would not have met Herman Goldstine on a train platform-von Neumann was not the man to invent the computer, but he was the man to understand its history and its potential. Indeed, von Neumann might never have left Germany. And instead of joining the army, Goldstine might have whiled away many quiet academic years teaching.

The computer I am typing on came to me in a certain way. The seed was planted and its shoot was cultivated by John Vincent Atanasoff and Clifford Berry, but because Iowa State was a land-grant college, it was far from the mainstream. Because the administration at Iowa State did not understand the significance of the machine in the bas.e.m.e.nt of the physics building, John Mauchly was as essential to my computer as Atanasoff was-it was Mauchly who transplanted the shoot from the bas.e.m.e.nt nursery to the luxurious greenhouse of the Moore School. It was Mauchly who in spite of his later testimony was enthusiastic, did know enough to see what Atanasoff had done, was interested enough to pursue it. Other than Clifford Berry and a handful of graduate students, no one else was. Without Mauchly, Atanasoff would have been in the same position as Konrad Zuse and Tommy Flowers-his machine just a rumor or a distant memory.

John Vincent Atanasoff was a lucky man in many ways. He lived to see his hard work and enterprising intelligence vindicated. He spent a long life trying many things and, because of his energy, organizational skills, and persistence, mastering everything he tried. Perhaps Atanasoff would have said that he succeeded in doing something very rare, which is doing what he wanted to do in the way he wanted to do it and discovering that the way he wanted to do it was, indeed, the best way. Kirwan c.o.x points out that what happened to the ABC also had much to do with Atanasoff's personality: "Mauchly was the only person to be shown the computer in such detail. Why? Atanasoff had a tendency to focus on something, and then he did it and moved on. Mauchly encountered him just at the moment he was most enthusiastic." c.o.x calls him the "lone inventor" type, who explores and invents and then exhausts his interest in a given idea. Money and fame are secondary to pa.s.sionate curiosity.

The question remains: would the computer as we know it have been invented without Atanasoff? I do not think ENIAC would have been; therefore, the computers that grew out of ENIAC and John von Neumann's thoughts about ENIAC might not have been invented. When Konrad Zuse found himself in the mountains at the Austrian border and pondered his future testing the fat content of milk at the local dairies, he heard from IBM-they were interested in his ideas-but they might not have been had they not felt the p.r.i.c.k of computer development in the United States. It does not seem as though Howard Aiken's decimal Mark IIV computers and those similar to it were likely to evolve very quickly into the small, powerful, and handy machines we have; the inventors devoted to a.n.a.log machines did not believe in electronic machines even when they saw them work. It does not seem likely, therefore, that they would have switched to electronic machines on their own. Tommy Flowers, Max Newman, and Alan Turing knew what electronics could do-it is possible that the computer industry could have blossomed in England rather than the United States, but even aside from the problem of British security concerns after the war (as far in philosophy from von Neumann's practice of encouraging and even forcing the sharing of information as it is possible to be), Colossus operated on different principles from the American computers designed originally to solve mathematical problems. On the other hand, if the ABC had not been invented, the need to solve very complex mathematical problems, especially those, at first, relating to the invention of the H-bomb, would have pressed mathematicians into some sort of calculating solution. The need was there. It would have been met at some point. But the ABC was invented, and as Kirwan c.o.x puts it, "The ideas [about computers] Atanasoff had were things that have continued to this day-the machine has been completely surpa.s.sed, but the concepts he had have not been surpa.s.sed."

For those of us who aren't mathematicians, inventors, physicists, or engineers, the history of the invention of the computer is a fascinating look at both human history and human character. There was no inventor of the computer who was not a vivid personality, and no two are alike. It is Alan Turing who has captured the imagination of the culture, perhaps because of his brilliant mind and his tragic death, but Konrad Zuse is at least as idiosyncratic, and his life was even more dramatic. Like Atanasoff, he lived until 1995, long enough to be remembered, and vindicated, too. The most poignant figure, in some ways, may be Tommy Flowers, who remains largely unsung. But perhaps our most problematic character is John von Neumann. Scott McCartney considers him a thief, Norman Macrae and Kati Marton consider him a visionary. Everyone considers him a genius. As for me, von Neumann is the man whose memoirs I would have liked to read, the man at the center of everything, the man of Budapest and the man of Was.h.i.+ngton, D.C. I would like to know who he thought had invented the computer.

Acknowledgments.

Thank you to the Sloan Foundation for funding this project. The invention of the computer is a wonderful story, and an important one.

Thank you to William Silag, for telling me this story the first time, in 1984, and for writing an article about Atanasoff in the Palimpsest, the Iowa history magazine, that year (and for plenty else, besides).

Thank you to John Gustafson, for much help in understanding all the issues, and for his contributions to the ma.n.u.script.

Thanks to Kirwan c.o.x, doc.u.mentary teacher/writer/researcher, who discussed information from the interviews and other research he has done for a television doc.u.mentary on John Atanasoff and the ABC, which is being produced by Eyesteelfilm, Montreal, for History Television in Canada.

Thank you to Robert Armstead, for editing and information.

All mistakes are mine.

Appendices.

John Gustafson, PhD.

Appendix A | Linear Solvers.

The problem that motivated John Atanasoff to build an electronic computer was one that had challenged mathematicians for many centuries. In about 300 BC, a Babylonian clay tablet gives this example of how a system of two equations can arise: There are two fields whose total area is 1,800 square yards. One produces grain at the rate of 2/3 of a bushel per square yard while the other produces grain at the rate of 1/2 a bushel per square yard. If the total yield is 1,100 bushels, what is the size of each field?*

Translated into equations, with x and y for the areas of each field, this word problem says that x + y = 1,800 square yards 2/3x + 1/2y = 1,100 bushels The Chinese also studied such problems, and in the Jiuzhang Suanshu, or Nine Chapters on the Mathematical Art, they provided examples of systems involving up to six equations in six unknown quant.i.ties as early as 200 BC.

Even though such problems could be posed very easily, the effort to solve them seemed extraordinary and out of proportion to the simplicity of the statement of the problem. At the risk of reminding the reader of some of the more tedious moments spent in middle school algebra cla.s.s, the way to solve the above system of two equations is to scale one equation so that the number multiplying x or y in one equation matches that of the other equation, and then subtract the equations to eliminate that variable. If we multiply both sides of the first equation by 2/3, for example, the two equations line up nicely: 2/3x + 2/3y = 1,200 2/3x + 1/2y = 1,100 and we can subtract the second equation from the first to get a system that involves only y: 1/6y = 100 This is called "forward elimination," where you eliminate one variable at a time from the system. After that, you "backsolve"; in the example above, y must be 600, and we can use the first equation x + y = 1,800 to conclude that x = 1,200.

What stymied human calculators was that the work to eliminate every variable grew as the cube of the number of equations. In the two-by-two example above, all one had to do was scale the first equation and subtract it from the second. But in a six-by-six problem (the largest one attempted in the Chinese tome), the first equation would have to be scaled for each of the other equations to eliminate that first unknown variable, and that task requires the performing of arithmetic on the entire six-by-six problem description (thirty-six numbers). That leaves a problem with five equations in five unknowns, so one has to repeat the elimination task, until all that is left is a simple equation in one unknown quant.i.ty. The "forward elimination" to get to a simple problem of one equation in one unknown is like a pyramid of arithmetic work. For a system of n equations, the base of the pyramid of work is n by n, working up to a tip that is 1 by 1, and the volume of that pyramid (the total amount of work) is proportional to the cube of n. (The backsolving task is still tedious, but only grows as the square of n.) In the 1700s, to solve even ten equations in ten unknowns was considered a nearly insurmountable task. It requires more than three thousand multiplications and subtractions, and each arithmetic operation usually must be done with at least ten decimals of precision to avoid rounding errors that would make the result unacceptably inaccurate. The German mathematician Karl Friedrich Gauss needed to solve a system of six equations in the early 1800s when he was trying to plot the course of an observable asteroid, Pallas, and spent years grinding away at the numbers using a method almost identical to that explained by the Chinese two millennia earlier; that method now bears the name Gaussian elimination.

By 1836, Charles Babbage had conceived his mechanical (steam-powered) a.n.a.lytical Engine, and in pitching his plan for it to the funding agencies of his era, he led with the idea that it could be used to solve systems of equations: In the absence of a special engine for the purpose, the solution of large sets of simultaneous equations is a most laborious task, and a very expensive process indeed, when it has to be paid for, in the cases in which the result is imperatively needed.

When a physical problem demanded a logarithm, or a cosine, or for a physical quant.i.ty like energy to be calculated, it might have required a few dozen calculations per input quant.i.ty, and human calculators knew it was tedious work but not intractable. Solving systems