# Ann Varela: Who was John von Neumann: And what did he have to do with the Atomic Bomb?

An Interview with Ann Varela: Who was John von Neumann: And what did he have to do with the Atomic Bomb?

Michael F. Shaughnessy –

1) Ann, the famous scholar John von Neumann was born around the turn of the century- around 1903- where was he born, and exactly when and do we know anything about his childhood?

Miksa and Margit Neumann were living in Budapest, Hungary when they welcomed their first-born son, János, into their home on December 28, 1903. The family of three eventually became a family of five with the addition of two more sons.

Von Neumann’s father was a wealthy banker who also had a law degree. Von Neumann’s mother’s family became well-off by selling farm equipment. The von Neumann family occupied a large 18-room apartment above the business office of his mother’s family where they nurtured their children with both Jewish and Christian customs.

Von Neumann displayed astonishing talents as a young child. He divided two 8-digit numbers in his head, spoke five different languages, studied differential and integral calculus, and read at a voracious rate. Von Neumann’s apartment had extensive bookshelves built in. A few sources even state that von Neumann could memorize and recite information from the telephone directory to entertain guests.

He and his brothers and cousins were all educated by governesses until the age of 10. Hungary’s institutional education was only available for children aged 10 and older. Eventually, von Neumann began his studies at the Lutheran Gymnasium which was equivalent to our present day grade school through senior high school level.

Von Neumann had to compromise with his father concerning what his focus of training would be for his university studies. He actually attended two universities simultaneously in 1921. Von Neumann studied mathematics at the University of Budapest and chemistry at the University of Berlin. It is somewhat amusing and astonishing to note that he did not actually attend his classes for the University of Budapest, yet apparently he was able to do brilliant work on the mathematics examinations.

By 1926, von Neumann earned his degree in chemical engineering from the Technische Hochschule in Zürich. Concurrently, he earned his doctorate from the University of Budapest in mathematics. His thesis topic was set theory. Von Neumann lectured at both the University of Berlin and Hamburg before he began his postdoctoral studies at the University of Gӧttingen on a grant provided by the Rockefeller Foundation.

Before Von Neumann made his way to the United States to be a guest lecturer at Princeton University in New Jersey, he married his fiancée Marietta Kovesi in 1930. Within one year, von Neumann was promoted to full professor at Princeton.

2) This scholar wore many hats–he is regarded as an iconic mathematician, physicist, inventor, computer scientist, and polymath. Now briefly, in your mind, what are the main differences in each of these fields? And how do they really overlap and use the abundance of skills this scholar had?

Mathematicians look for patterns and use them to contrive new inferences. Mathematicians decide the certainty or inaccuracy of inferences by constructing mathematical proofs. When mathematical explanations are relatively good or accurate models of real-life events, then mathematical reasoning can provide understanding or projections regarding other environmental events.

Physicists study matter and its movement and behavior through time and space, together with related ideas such as energy and force. Physicists seek to understand how the physical universe works. Mathematics and computer science are also important subjects for physicists to study because those subjects are used to model theoretical physics.

As an inventor, one may develop an idea on paper, a computer, or construct a model. Inspiration may come from insight, exploration, improvement on an existing concept, or necessity.

Computer scientists specialize in the theory of computation and the design of computational systems.

As a polymath, von Neumann was able to connect ideas from a variety of disciplines. For example, game theory was connected to strategic war plans, binary code was applied to computer storage programs, and the Brouwer fixed-point theorem from topology was applied to economic theories of equilibrium.

3) Now, what exactly is a polymath? And where does it fit into mathematics?

Polymaths possess wide-ranging knowledge. As mentioned above, mathematical theories are used in several other disciplines. Disciplines are intertwined to enable new theories to develop as well as for old theories to be used in new applications. For example, people employed in a “think tank” need the skills of a polymath to further research and development of high-tech devices, advance performance of medical procedures and treatments, or improve crop production, to name a few. Mathematical models are frequently a part of improvements in other fields of study.

4) From my college days, I do believe that I remember that “numerical analysis” comes after Calculus 1,2,3 and 4–First of all, am I correct here- and what exactly is numerical analysis and do you know HIS contributions to this field?

The prerequisite courses for Numerical Analysis typically involve Calculus II and Computer Science I. Numerical analysis studies algorithms that use numerical approximations for the problems of mathematical analysis. An algorithm is basically a set of rules that specifically defines a progression of operations which may be comprised of either a calculation, data processing, or programmed reasoning tasks. Numerical analysis is concerned with finding approximate solutions while preserving reasonable constraints on miscalculations. Exact solutions are not the focus in numerical analysis.

Von Neumann created stability analysis which is also known as Fourier stability analysis. This procedure is used to check the stability of finite difference schemes as applied to linear partial differential equations. The three types of stability which may result with the application of stability analysis include: stable (errors made at one increment of the calculation do not cause the errors to be amplified as the calculations are continued), neutral (errors remain uniform as the computations are continued), and unstable (errors escalate with time).

5) Now, what is functional analysis? And why is it important?

Functional analysis studies vector spaces and mappings (operators or functionals) between them. Most spaces studied in functional analysis are infinite-dimensional. This branch of mathematics is important because it allows one to make projections or approximations concerning the behavior of objects and deformations by mechanical forces acting on elastic bodies including stretchable membranes like plastics, ice, and metals. Functional analysis is used to examine the vibration of a circular drum head. See Figure 1.

Figure 1

https://upload.wikimedia.org/wikipedia/commons/6/6f/Drum_vibration_mode22.gif

Click on the link to see the animation.

6) I have heard the term “ergodic theory” but have no real comprehension as to its relevance. Can you enlighten us?

Ergodic theory is a field of mathematics that studies dynamical systems (systems in which a function describes the time dependence of a point in a geometrical space) with an invariant measure and related problems. In other words, the dynamic system follows a rule that states that there is an implied relation that gives the status of the system for only a short time into the future. The relation could be a differential equation, difference equation or some other time scale. To determine the status for all future times requires iterating the relation numerous times, each progressing time at slight increments. The iteration process itself signifies solving the system.

Mathematical representations that describe the swinging of a clock pendulum and the flow of liquid in a pipe are some examples of dynamical systems. The Lorenz system is another example of a dynamical system. The Lorenz system is a system of ordinary differential equations which has disordered solutions for certain parameter values and initial conditions. At some point in time the dynamic system will look like a butterfly, while another point in time results in a figure-eight. See Figure 2.

Figure 2

Click on the link to see an interactive video of the Lorenz system.

https://upload.wikimedia.org/wikipedia/commons/e/ea/A_Lorenz_system.ogv

7) Some interesting tidbits- I have read that he had an extreme fear of Russians and the Soviet Union. Did this stem from his childhood, or some other event?

Von Neumann believed in “preventive war” when it came to the Russians, which seems to mean “bomb them before they can bomb us.” He felt strongly about the notion of the Soviets having spies gathering intelligence about the design of the atom bomb. However, by 1953, the Soviets already had hundreds of warheads. Retaliation was now a possibility.

8) I understand he was partially involved in the atomic bomb- do we have documentation as to the degree of his involvement?

Von Neumann’s main contribution to the atomic bomb itself was theory and blueprints for the explosive lenses needed to condense the plutonium core of the Trinity site test device. Von Neumann’s hydrogen bomb work was also applied in the field of computing. Von Neumann and Stanislaw Ulam made the necessary hydrodynamic computations on von Neumann’s digital computers.

9) His greatest contribution- I suppose there would always be discussion about this–but in your mind- what were his greatest contributions?

I think it is unfortunate that the advancements made in the field of computer science at that time were the result of creating an atomic bomb first. But the saying goes, “necessity is the mother of invention.”

Von Neumann was able to develop machines for the calculation of numbers and the resolution of mathematical applications during his work on the atomic bomb which ultimately helped to shape the foundation of our modern-day computers.

Perhaps another important contribution of von Neumann’s is his work in the field of functional analysis. After all, if surgeons and developers of medical implants did not know how implanted mesh materials, (such as the ones used in hernia repair, temporary support of organs, reconstructive work, or tissue repair) would behave in the human body, some of us would literally be in a world of hurt.

10) His later years- how were they spent?

After the war, von Neumann spent much of his time as a government consultant. He made important contributions to the U.S. Army’s Electronic Numerical Integrator and Computer, in that he modified ENIAC to run as a stored-program machine. The ENIAC was used to research the viability of the hydrogen bomb and for the world’s first numerical weather forecasts. ENIAC was the first programmable general-purpose electronic digital computer. See Figure 3.

Figure 3

https://media1.britannica.com/eb-media/95/170195-004-89A6EABB.jpg

Von Neumann suggested the utilization of binary code for storage of data when he made improvements in the design of a new machine for the Institute for Advanced Study around 1945.

11) What have I neglected to ask?

I think that most people associate von Neumann’s computer related efforts and explosive lens designs, which were developed during WWII, with his most significant contributions to the war effort; however, he also applied game theory to military battle strategies which led to the allies’ triumph.

John von Neumann also received numerous awards for his discoveries and contributions to mathematics, computer science, and science, such as the Enrico Fermi Award, the Presidential Medal of Freedom, the Bocher Prize, and the Albert Einstein Commemorative Award.