by Kurt W Beyer
In the fall of 1941, Hopper began to work closely with Courant in the emerging field of partial differential equations. This particular type of equation was the mathematical foundation for an array of cutting-edge scientific and engineering disciplines, including aerodynamics (the study of gases in motion), hydrodynamics (liquids in motion), electrical engineering, and quantum mechanics. These techniques could be applied to, among other things, aircraft design, weather prediction, traffic flow, and the propagation of radio waves.
Hopper admired Courant’s mathematical genius, and she gained from him the ability to glimpse at the obscured numerical tapestry underpinning the physical world. “He [was] just one of the most delightful people to study with I’ve ever known in my life,” she recalled, “Of course, he scolded me at intervals . . . because I kept on doing unorthodox things and wanted to tackle unorthodox problems.”15 But after Japan attacked Pearl Harbor, the lighthearted mood of the NYU mathematics department changed. For the rest of her time there, Hopper’s work was dedicated to somber problems concerning national defense.
IN SEARCH OF A NEW PATH
“I finished that year [with Courant], and then of course when we were in the thick of it, my brother and my husband and everyone wanted in,” Hopper recalled.16 Vincent Hopper left NYU and desperately tried to get an officer’s commission. Because of his age and his poor eyesight, he was rejected. Grace’s brother Roger, who had just completed a doctorate in economics, also had poor eyesight. Both men then put their promising academic and business careers on hold and enlisted. Both served the entire extent of the war in the Army Air Corps, Roger Murray eventually receiving a commission and rising to the rank of captain.17
By the summer of 1942, Grace Hopper’s husband, her brother, her cousins, and many of her friends had joined the military. “Our whole family was in,” she recalled. “Everybody except my sister, who had small children and wasn’t acceptable.”18 Grace, too, aimed to do her part. In the summer of 1942, not wanting to go back to Vassar, she took a position at Barnard College, where she taught an improvised summer school course designed to prepare mathematicians for the war effort.19 The unprecedented attack on American soil had awakened a deep patriotism in Grace and others, but traumatic events also affect individuals on a deeper level. Often they lead to introspection. For Grace, Pearl Harbor became the external catalyst that led to a series of changes in her personal life.
Though her tenured position at Vassar appeared ideal, deep down Grace wanted to escape a job that was secure and respected but no longer challenging. She wanted to break away from the mundane 75-mile commute to Poughkeepsie from New York City, and from the 35 summers she had spent with family members in New Hampshire. At last facing the fact that her marriage had failed, she decided to leave everything behind and join the Navy.
On 30 July 1942, President Roosevelt signed the Navy Women’s Reserve Act, which authorized the formation of the WAVES (Women Accepted for Volunteer Emergency Service). WAVES were assigned to non-combat positions as aircraft mechanics, pilots, radio operators, medical personnel, and so on. Mildred McAfee, president of Wellesley College, was named the new organization’s first director. By 1945 the WAVES numbered 8,000 officers and 76,000 enlisted personnel.20
Hopper returned to Vassar in the fall, but she had lost the desire to teach undergraduates. “I was beginning to feel pretty isolated sitting up there, the comfortable college professor,” she recalled. “All I was doing was more teaching, and I wanted very badly to get in [to the Navy], so I finally gave Vassar an ultimatum that if they wouldn’t release me I would stay out of work for 6 months because I was going into the Navy, period.”21
The dissatisfied mathematician eventually arranged a leave of absence from her teaching position, but she quickly discovered that joining the Navy was not a simple matter. Aside from the fact that she was considered too old and too small for naval service, her chosen profession as a mathematics professor had been declared crucial to the war effort. Undeterred, Hopper obtained waivers for her weight and age. In December 1943, on the eve of her 37th birthday, she reported to the United States Naval Reserve Midshipmen’s School in Northampton, Massachusetts.
Midshipmen’s School, designed to transform civilians into future naval officers, was a harrowing experience for most young recruits. “When we first got there we had to pack up all of our civilian clothes and ship them home,” Hopper recalled. “They wouldn’t let us wear silk, so we had to wear those horrible [cotton] stockings.”22 Recruits were fitted for uniforms (cotton stockings and all), given haircuts, and separated from their family and friends. The first days were dedicated to learning proper military protocol: how to wear a uniform, how to carry oneself, how to address superiors and subordinates. Each recruit was expected to memorize a wide assortment of facts and figures, including the ranks and rates of officers and enlisted personnel and the names and capabilities of various ships and weapon systems.
The training environment was deliberately made stressful in order to fortify a recruit’s resolve when faced with obstacles. Amenities were few, personal time limited, and opportunities for sleep and relaxation restricted. In the classroom, Hopper and her peers learned about naval history, navigation, tactics, naval organization, and the basic principles of leadership. Naval etiquette, from wearing the proper attire at functions to the correct way to write business letters, was also emphasized.23 Despite all the rigors, Midshipman Grace Hopper remembered an unexpectedly pleasant experience:
When I got there I’d been teaching all these courses, doing all this outside work, running back and forth from New York to Poughkeepsie and teaching at Barnard and Vassar and umpteen other things trying to take courses, write stuff . . . and all of a sudden, I didn’t have to decide anything, it was all settled. I didn’t even have to bother to decide what I was going to wear in the morning; it was there. I just picked it up and put it on. So for me all of a sudden I was relieved of all minor decisions. All the minor stuff was gone. I didn’t even have to figure out what I was going to cook for dinner. . . . It’s all gone, and I just reveled in it. I had the most complete freedom I’d ever had. . . . I just promptly relaxed into it like a featherbed and gained weight and had a perfectly heavenly time.24
Midshipmen’s School was so agreeable to Hopper, in fact, that she was named battalion commander, the highest-ranking position within the school. She graduated first in her class.
THE FIRST DAY OF THE REST OF HER LIFE
When Lieutenant (junior grade) Grace Hopper graduated from Midshipmen’s School, in the summer of 1944, it became the responsibility of the Bureau of Naval Personnel in Washington to decide how best to utilize her talents. During peacetime, assignment decisions usually took into consideration the desires of the officer in question. But during wartime, the needs of the Navy usually superseded the needs and wants of the individual.
When Hopper entered officer training, she was under the impression that upon graduation she would be assigned to the Navy Communications Annex. The Communication Annex consisted of a covert cadre of mathematicians and logicians tasked with breaking enemy codes. Modern warfare’s dependence on wireless communications for command and control augmented the status of these technical elites, for knowledge gleaned from intercepted enemy communications could influence a war’s outcome as much as traditional determinants such as superior weaponry and manpower. It seemed logical that Hopper’s mathematical expertise would best serve the war effort in such a capacity. Furthermore, the head of the Communication Annex, Captain Howard Engstrom, had been one of Hopper’s mathematics professors at Yale. “I had talked to Engstrom, and so far as I knew it was set up that I would be assigned to the Communications Annex,” she recalled. In fact, during the fall of 1943,
Grace Hopper on the day of her graduation from the Naval Reserve Midshipmen’s School in Northampton, Massachusetts, 27 June 1944. Courtesy of Archives Center, National Museum of American History, Smithsonian Institution.
while Hopper was waiting for
her age and weight waivers, she took a course in cryptographic analysis in preparation for working with Engstrom.25 But while Hopper had been at Midshipmen’s School, a one-of-a-kind calculating machine had been shipped to Harvard University from IBM’s laboratory in Endicott, New York. The mysterious machine, placed under the auspices of the Navy’s Bureau of Ships, was a computer, though it was not called that at the time. “Instead of being ordered to the Communications Annex, I was ordered to Harvard, and my orders were changed during the time I was at Midshipmen’s School,” Hopper stated.26 Through no choice of her own, Lieutenant (j.g.) Grace Hopper was about to become the third programmer of the world’s first computer.
The Automatic Sequence Controlled Calculator, as the machine was officially called, was the brainchild of Lieutenant Commander Howard Aiken.27 Before the war, Aiken had been a physics graduate student at Harvard. While working on his dissertation, he had formulated plans for a distinctive mechanical arithmetic machine. The concept was supposedly born out of Aiken’s aggravation as he struggled through the calculations that supported his doctoral thesis on the propagation of radio waves. The scope and complexity of the mathematics that describe Aiken’s work weighed down upon the physicist, and even a small sampling would have taken him years to work out by hand. Aiken’s practical disposition led him to consider the possibility of automating the calculating process, and in 1937 he began privately circulating a paper titled “Proposed Automatic Calculating Machine.”28 The paper describes in detail Aiken’s vision of an automated arithmetic machine able to solve any problem that could be reduced to numerical analysis, including ordinary and non-linear differential equations.
The culmination of Aiken’s seven-year search for relief from tedious calculations stood 8 feet high, 3 feet wide, and 51 feet long, weighed 9,445 pounds, and had 530 miles of wiring. The Automatic Sequence Controlled Calculator, officially donated to Harvard University by the IBM Corporation on 7 August 1944, 29 was capable of addition, subtraction, multiplication, and division. It was also hard-wired for logarithms, trigonometric functions, and exponentials, much like today’s hand-held calculators. The massive machine’s most noteworthy feature, however, was a paper-tape mechanism. The tape was pre-coded with step-by-step instructions that dictated the machine’s operation and guided it toward a solution without the need for further human intervention. Aiken’s creation was one of the first examples of a programmable machine. Up to that time, machines had been passive tools used by humans to extend some human physical attribute, as a telescope or a typewriter does. Aiken endowed his machine with the ability to take autonomous action. Granted that a human had to specify the parameters of that action, the Automatic Sequence Controlled Calculator was intended to augment not the arm or the eye but the mind.
The newly dedicated Automatic Sequence Controlled Calculator (referred to by the Harvard crew as Mark I), 1944. Courtesy of Archives Center, National Museum of American History, Smithsonian Institution.
Mark I, as Aiken called the peculiar “land-based ship” he commanded,30 was now charged with a much more serious task than helping Aiken to complete his doctoral dissertation. It was a new type of secret weapon that could change the outcome of the war. It was to be used to calculate solutions for rocket trajectories, proximity fuses, and mines, and to generate tables of mathematical functions that could be used to solve general engineering problems ranging from radio wave propagation to ship hull design. Staffing these efforts had become Aiken’s main concern, and he had begun to seek out mathematicians who had joined the Navy. Lieutenant (j.g.) Grace Hopper seemed to fit the bill.
The original crew in charge of Mark I, August 1944. From left to right, top: Seaman Bissell, Seaman Calvin, Seaman Verdonck; bottom: Ensign Bloch, Lieutenant Commander Arnold, Commander Aiken, Lieutenant (j.g.) Hopper, Ensign Campbell. Courtesy of Archives Center, National Museum of American History, Smithsonian Institution.
Hopper reported to Aiken’s Harvard command in the basement of Harvard University’s Cruft Physics Laboratory on 2 July 1944. If being escorted down to the basement by an armed guard wasn’t disquieting enough, the presence of her physically intimidating boss was. “I was a little bewildered and at that point of course thoroughly scared,” Hopper recalled. Years later, she distinctly remembered the first words uttered to her by Aiken: “Where have you been?” Aiken had expected Hopper months earlier and had not seen the point of sending a female mathematician to Midshipmen’s School.31
Aiken proceeded to give his new recruit a tour of the Automatic Sequenced Controlled Calculator. Hopper arrived before IBM had installed the smooth steel casing, so the machine’s thousands of moving parts were fully exposed. “All I could do was look at it. I couldn’t think of anything to say at that point,” she remembered. At the end of the tour, Aiken ordered his new assistant to put off finding a place to live for another day and to get to work immediately. Her first task was to compute the interpolation coefficients for the arctangent to an accuracy of 23 decimal places within a week.32
Hopper’s frosty reception was an early indication of the antagonistic environment she had just entered. Howard Aiken was disappointed that the Navy had assigned him a female officer to be second in command, an opinion that he openly shared with the rest of the men on his staff. “Well, there was Aiken and then there was the boys,” recalled Robert Campbell, one of the two ensigns who arrived at the Computation Laboratory before Hopper.33 Richard Bloch, the other ensign, also shared Aiken’s misgivings. “I later found out that they [Campbell and Bloch] had been . . . trying to bribe each other as to which one would have the desk next to me,” Hopper recalled.34
Gender tensions aside, Hopper was faced with a technical obstacle of imposing proportions. Aiken had given her a week to solve a fairly straightforward math problem. Arctangents (the inverse of a tangent function) were covered in most high school geometry curricula and were child’s play for a former college mathematics professor. The issue was not the problem’s complexity, but its scope. Solving for a huge array of numbers to 23 decimal places was humanly impossible within the time frame Aiken had provided. To assist her, Hopper had to rely on a machine the likes of which she had never encountered. She could not turn to previous experience. She could not review work done on other calculating machines, since Mark I was unique.35 There was no manual of operation, and no customer support. In fact, Hopper did not even know how to refer to her new occupation; the term “programmer” would not enter the language until years later.36
“Well, they gave me a code book and told me to do it,” Hopper recalled.37 The “code book” was a crudely tabulated notebook containing instructional codes for the machine. To the untrained eye, the notebook was nothing more than a list of unintelligible numbers. Robert Campbell had quickly thrown it together in the spring of 1944 while running test problems on Mark I after it was brought from IBM’s laboratory in Endicott to Harvard.
Not only was Campbell Mark I’s first programmer; during 1943 and the first half of 1944 he also served as manager of the project. Aiken had been called up to active duty and assigned to the Naval Mine Warfare School in Yorktown, Virginia. Aiken had chosen the clever young physicist from a list of Harvard graduate students, and during his absence Campbell oversaw the completion of the machine, kept Aiken informed, and served as the bridge between Harvard and IBM. Upon Aiken’s return, in May 1944, Campbell was commissioned an ensign in the Naval Reserve and became a full-time member of Aiken’s staff.38
The techniques Campbell had compiled in the “code book” had been gleaned during the programming of the initial three problems. The first problem (referred to simply as Problem A39) involved solving trigonometric functions in connection with antenna design for Professor Ronald King of Harvard’s Physics Department.40 Problem B, requested by the astronomer and telescope lens designer James Baker, concerned refraction angles for rays passing through a multi-component optical system. Problem C, requested by the Navy Bureau of Ships, concerned the effects of small impurities o
n the physical characteristics of steel. Problem C, in particular, demonstrated to Campbell the true power and potential of the machine, as ten equations were solved simultaneously.41
Hopper quickly recognized that to succeed in communicating with Mark I she would have to rely on the experience that Bob Campbell and Richard Bloch had acquired. “Whenever I got in trouble, I would yell at Bloch and Campbell and [they] would tell me how to get out of it,” Hopper remembered.42 Bloch also recalled those early days tutoring the “professor”: “I remember sitting down . . . long into the night, going over how this machine worked, how to program this thing, and so on. As I like to remind her, she didn’t know a computer from a tomato basket at the time.”43 In fact, as of July 1944 the 23-year-old Bloch knew little more than his pupil; he had acquired only 3 months of coding experience before Hopper’s arrival.
What Bloch lacked in experience he made up for in drive and determination. A consummate overachiever, he had majored in mathematics, minored in physics, and played in the Harvard band, and in 1941 he had won the Dexter Award for the top-ranking freshman. Bloch envisioned becoming a college professor, but (as happened for so many young men of his generation) the repercussions of Pearl Harbor translated into an unintended career choice. Upon graduation, he reported for midshipman training at the University of Notre Dame in Indiana, and in September 1943 he was stationed at the Naval Research Laboratory in Washington. “We all wanted to do our thing, and my idea was to get on the biggest ship possible, so I applied for duty as a navigator on a battleship,” he recalled.44 Upon review, the Bureau of Naval Personnel concluded that Bloch’s mathematical aptitude would best serve the war effort if applied to analytic and computational work associated with antenna design in the Naval Research Laboratory’s Radio Division.
