Technical War Work, March-December 1944

Following the closure of the NRPB, Samuelson’s visits to Washington ceased and his activities at MIT increased. In March 1944, he wrote to his friend Walter Salant, “Except for a visit of 2 hours, I have not been to Washington since last June.

On Saturday, March 18, Compton discussed with Samuelson the possibil­ity of his working for the Office of Field Services (OFS). This was a division within the Office of Scientific Research and Development (OSRD), headed by Vannevar Bush, and from 1943 to 1945, Compton was its director.^a The following Tuesday, Samuelson wrote to Compton, saying that he had reached the conclusion that he should instead move to MIT’s Radiation Laboratory, the reason being that his “past activities in testing anti-aircraft” made him think his comparative advantage lay in carrying on with this work.² It is not clear where or when he had done such work. One possibility is that mathematical

a. There is no indication of the work he was offered. problems related to fire control were covered in the teaching of navy officers that he had been doing for the mathematics department. Another is that his contact with Norbert Wiener had caused him to think about the problem of fire control. Wiener ran, with physiologist Arturo Rosenblueth, an inter­disciplinary seminar in which the theory of cybernetics was developed, and at some date between 1937 and 1942, Samuelson began attending.^3b These seminars covered physiology—a topic to which Samuelson had been intro­duced by Lawrence Henderson—and machines, and involved problems of information feedback and control.

On the same day as Samuelson spoke with Compton, he also wrote his local draft board, saying that he had been released from his instructional duties so as to take on duties of a full-time staff member in the Radiation Laboratory to do work described as “[r]esearch and development of highly secret military devices in the field of high frequency electronics.”⁵ He started work the next day, on March 22, 1944, in the Theory Group, Mathematics and Statistics, working on “[d]esign and research in fire control problems.”⁶ He told Abram Bergson that he found it “quite exciting,” though it was “very strenuous and working from 8:30 to 6 leaves me little time for the economic reading which I should like to do. In fact, it is only with the greatest effort that I am able to make progress on the remaining chapters of my own manuscript."^7,c Given that he had been working there for just two weeks, it suggests he had under­estimated how time-consuming his work there would be.

In the Radiation Laboratory, Samuelson was a member of Ivan Getting's Fire Control Division. Getting, almost three years older than Samuelson, had graduated from MIT in 1933, before taking a doctorate in astrophysics

b. Karl Deutsch, a historian and political scientist who arrived at MIT in 1942, wrote, “In Wiener's informal ‘seminar' in the backroom of a nearby restaurant these young scientists, as well as Paul Samuelson, Jerome Wiesner, Frank Piore, Julius Stratton and other research leaders[,] would take part in these discussions which were a great experience for me" (Deutsch 1980, p.

c. This refers to the revision of his thesis, discussed in chapter 22 this volume.

at Oxford. He then became a junior fellow at Harvard, overlapping with Samuelson for three years. In 1940, he had joined the Radiation Laboratory, co-directing the project that developed the SCR584 radar which, brought into service late in 1943, greatly improved the army's ability to track and shoot down enemy aircraft. Following this success, in 1943 he turned to developing the Mark 56 gunfire control system for the U.S. Navy. The goal of this project was to make it possible for a ship's guns to be fired “blind,” able to hit targets at night or when fog or atmospheric conditions made seeing them impossible. Aiming for a completely automatic system was conceptu­ally and bureaucratically very ambitious, for Getting believed that to achieve this goal, it was necessary to control both the design and the production of the system. The system was first tested in the spring of 1944, with the first automatic firing of live ammunition taking place the following December.⁸

Samuelson was part of a theoretical section that included the logician and cognitive scientist Walter Pitts, who had recently proposed a math­ematical model of a neural network and who had come to Cambridge to work with Norbert Wiener.⁹ Their focus was on entire systems, this being one of the reasons why Getting had went to considerable lengths to get control of all aspects of the project—something in which he was not com­pletely successful.¹⁰ It was necessary to integrate analysis of ballistics with understanding of the mechanical system and the human operator.

The details of Samuelson's activity within this group in which he worked long hours are unclear, no doubt because the classified nature of the work precluded his leaving a paper record of what he was doing. When writing to colleagues, declining their invitations to take on work, he obviously took pride in being able to explain that he was engaged in classified, technical war work.

One surviving draft shows Samuelson taking a broad view of the fire control system: “A Suggestion for a Generalized Fire Control Correction Box.”¹² This looked at the general problem of attacking a moving target. It was a mathematical problem involving predictions in which the relevant variables were determined simultaneously. That is, if a shell were being fired at a moving target (and for long-range guns, the movement of the earth may also need to be taken into account), the position of the target when the shell arrived (assuming it is to be hit successfully) depended on the time it took for the shell to travel to its destination; but this time depended on where the target would be, so the solution involved solving a pair of simul­taneous differential equations. This was inherent in the problem and had to be solved with some sort of dynamical feedback mechanism. Samuelson assumed that the target was moving in a straight line, so that its position could be calculated from its initial position, as well as its velocity and the time the shell took to reach the target. This time was determined by ballis­tic considerations including the type of shell, its initial velocity, air density, and the direction in which the gun was aimed. In solving these two equa­tions, a formula could be found that related the direction in which the gun was aimed to various positions and velocities. Samuelson did not actually solve such a system, but he described the equations using abstract functions, deriving its properties.

This was the simplest version of the problem, for in practice it would be necessary to take into account the movement of the ship on which the gun and the gun director (the radar) were placed, wind, and parallax effects aris­ing from the gun director’s not being in exactly the same place as the gun (there was expected to be one radar set controlling guns placed in different places on the ship). The box he was proposing was concerned with dynamic corrections—ones that depended on the motion of the target. He explained the importance of such dynamic corrections with an example.

To return to the example of horizontal parallax, imagine a torpedo bomber which is crossing the bow of a ship some 2000 yards ahead at the rate of 150 yards per second. If the gun is further from the target than the director, it will not suffice to change the fuse setting in the hope of preventing the shell from going off between the ship and the target. By lengthening fuse setting we can make it go off in the previ­ous predicted position. But still this will be too late, the plane will have gone past already. Actually the proper dynamic correction will result in a new fuse setting and in a new lead angle.¹³

This meant that the ideal was to recompute the problem taking into account the corrected data.

The problem was that this was not always possible. The Mark 56 direc­tor, as it stood, did not allow for certain factors such as variable air densities. More important, the effects of disturbances might be different for different guns served by the same director. Corrections would be different for 5-inch and 400-millimeter shells, and would be different if the objective was to aim two guns at two different aircraft in a formation. Samuelson then developed the theory of the correction box, which involved differentiating the equations describing the motion of the system and solving for the changes to the shell's flight time (which might be needed to set a fuse) and the direction in which the gun needed to be fired.

The paper, intended for circulation only to specialists familiar with the project, gave no indication of the relationship of Samuelson's work to that of his colleagues. It is possible that the idea of a correction box was Samuelson's idea for solving a problem that members of the unit had identified, or even that it was Samuelson who had identified reasons why the existing director would fail to work as required, though given Getting's experience of such problems, this seems unlikely. It is more likely that others, perhaps Getting, had identified the problem and that Samuelson had been tasked with work­ing out the theory of such a correction box. Whichever of these is correct, the paper makes it clear that Samuelson was thinking about the system as a whole, and was not just working on mechanical calculations.

Two other papers show Samuelson tackling narrower problems. “Differential Corrections in Anti-Aircraft Trajectories” was concerned with finding a simpler method for solving differential equations so as to reduce the number of calculations that needed to be done, a critical problem given the absence of powerful computers and the need for calculations to be done at great speed.¹⁴ The other paper was completely different in character—a sta­tistical analysis of tracking data, circulated as a Radiation Laboratory report. By this time, a prototype of the Mark 56 director existed and before testing with live ammunition, the accuracy of the mechanical apparatus was being tested using a motion picture camera mounted on the radar dish to record “the actual elevation and traverse position errors.” The paper's abstract read as follows:

Breadboard model of the gun director Mk 56, mod. 0, angular posi­tion errors and gyro torque motor rate currents have been subjected to statistical analysis and examined for consistency. Autocorrelation, rectangular smoothed rates, double exponential smoothed rates, mean square errors, and other statistics have been calculated.

On all four of the courses analyzed the root mean square error in traverse rates smoothed for 1.5 seconds was 0.7 mil/sec or less. On the one course subjected to intensive comparisons it would appear that the rates derived from the gyro current are fairly consistent representa­tions of rates as derived from position data.¹⁵

This was a nontrivial statistical problem because data were measured sub­ject to error, with the result that they had to be smoothed using a variety of methods. Once again, the need to economize on calculations was a major con­straint. Samuelson noted that it was possible to take a short-cut, noting that there was a relationship between the error they were trying to measure and the auto-correlation function, a statistic that was comparatively easy to cal­culate, thereby avoiding a more complicated set of calculations. Five pages of text were followed by twenty-three pages of graphs. Unlike the other papers, this was clearly one in which he had a team of assistants to complete the com­putations. His conclusion was that “this is good tracking.”

Samuelson was impressed by his colleagues and their mathematical abili­ties. His later remark that working at the Radiation Laboratory was the first time he experienced a situation in which he was not the brightest person in the room may even indicate that this was a shock to his self-confidence.¹⁶ However, although it was a project controlled by physicists and engineers who had skills with which he could compete, it was also one to which bright outsiders, such as Samuelson and Pitts, could contribute. His mathemati­cal knowledge—of statistics, differential equations, and the theory of equa­tions—was important, but he was not working simply as a mathematician. Had that been the case, he would not have had to visit the Naval Research Laboratory. To be able to analyze the system and work out the theory of a cor­rection box, the ability to make the link between the mathematical analysis and the physical problem was just as important.

Though working long days as a mathematician, he was never cut off from his economist friends and colleagues. In June 1944, he described what was going on in Cambridge to a former student, Bob Roosa.

Things in Cambridge go on very much the same. I am now on full­time leave from the Department working on hush-hush matters at the Radiation Laboratory. There is not very much instruction in econom­ics on the graduate level these days, I guess, but the undergraduate teaching load seems to be holding up. Bob Bishop, Art Bright, and Vandermeulen are still around and most of the members of the perma­nent staff are also here, in between their many important consultations with various and sundry important groups.

Except for the fact that all the students are Chinese and South American, Harvard proceeds along its usual way. Hansen is on the same old schedule, Haberler, who was at the Federal Reserve, is returning, Harris is full-time in Cambridge and is writing no less than four (4) books. Schumpeter is in residence except during the summer months, however, we haven't seen very much of him. Burbie is again chairman of the department.

This spring there has been a series of evening lectures at Littauer during which numerous visiting experts discussed problems of recon­struction. On the whole they were not too good. As usual, Williams, in his comments upon the speakers, started out brilliantly but unfor­tunately he had to begin repeating himself before the series was well underway and so the result was something of an anticlimax. Believe it or not, he talks now of the necessity for getting consumption up, but he doesn't say how it's to be done; and he seems really to believe that with the vast technological productivity of American industry, unem­ployment is inevitable.¹⁷

Samuelson's time in the Radiation Laboratory was very important to him. This was not just because it involved making a contribution to the war effort that justified his not being in the army. He had always been concerned with science, and here he worked closely with physicists and mathematicians on a major project. It was salutary for him to mix with such people who made him aware of his own limitations. He always stressed the long hours and the hard work involved, well aware that many of his contemporaries in the armed forces were facing much worse. He remembered being bored by the work, perhaps because he knew it was an environment in which he could not excel, claiming that “by 4 pm my slide rule seemed heavy and I would play hookey in MIT's math library.”¹⁸ His workload was not so heavy that it prevented him from continuing to work as an economist. He attended lectures and seminars at Harvard, and although his teaching at MIT was suspended, he continued to teach at the Fletcher School; he also continued to revise his thesis for publication, worked informally as a consultant to the War Production Board, and took his first steps into journalism.^d The work also meant that his position at MIT became much more than that of a member of a comparatively marginal department: he was doing work that was central to MIT's activities, work that could be understood by the scientists who were in control of the institution. He also became interested in the problem

d. See chapters 22 and 23 this volume. of government policy toward science, probably because he discussed what was going on in the Radiation Laboratory with its official historian, Henry Guerlac, a historian of science who had overlapped with him in the Society of Fellows. This became more than a passing interest, and grew to take up a significant portion of his time.