Dec 282017

Today is the birthday (1903) of John von Neumann (born, Neumann János Lajos) legendary mathematician who could well lay claim to being the greatest mathematician of all time, if I were given to superlatives. He made major contributions to a number of fields, including pure mathematics (foundations of mathematics, functional analysis, ergodic theory, representation theory, operator algebras, geometry, topology, and numerical analysis), physics (quantum mechanics, hydrodynamics, and quantum statistical mechanics), economics (game theory), computing (Von Neumann architecture, linear programming, self-replicating machines, stochastic computing), and statistics. Quite a mouthful. Next to von Neumann, the iconic genius, Einstein, who had an office down the hall from von Neumann at Princeton for many years, was second rate. Yet von Neumann tends to be forgotten in the popular mind these days, except perhaps indirectly when people refer to a “zero-sum game” which was a small part of the game theory he invented.

Writing something both interesting and useful – as well as being brief –  about von Neumann is a real challenge. I won’t say too much about his mathematical genius except to say that he was the rare person, indeed, who could see mathematical problems in their totality almost instantly, and could solve them almost as fast, because, unlike most other mathematical geniuses, he usually did not have to wade through calculations to find a solution, but could see the big picture with paths leading in and out intuitively. Such a mathematical mind does not come along very often.

Georg Pólya wrote that von Neumann was,

The only student of mine I was ever intimidated by. He was so quick. There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn’t say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann.

I’m not sure whether I would include von Neumann on my list of people (alive or dead) I would like to have dinner with.  By all accounts he had a decent sense of humor, and was a good storyteller, but he could also be crudely insensitive, and tell off-color jokes without concern that he might offend.  His interest in women was strictly sexual, and the secretaries at Los Alamos had to put cardboard modesty screens on the front of their desks because he would quite blatantly ogle their legs when he was in the room even though he was a married man. I would go as far as to say that despite being an exceptionally intelligent man, he had little grasp of certain fundamental principles of living. In fact, he acknowledged as much on many occasions.  This famous quote may be the most telling:

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.

An interesting quote to parse on many levels. There is no doubt that van Neumann found mathematics simple, even mathematical problems that stumped great minds. By comparison, he thought that life was much more complex, and, by implication, cannot be reduced to mathematical models. At one point he said:

There probably is a God. Many things are easier to explain if there is than if there isn’t.

Von Neumann took Pascal’s wager when he was near death and embraced Catholicism, while being overtly agnostic all his life (even though he was baptized in 1930 after his father’s death and before he married, for convenience only). Pascal argued that if death is the end, then you lose nothing by being a Christian. But if death leads to heaven or hell, it would be much better to die a Christian than not. Either way you win. The small trick here, which von Neumann apparently did not allow for, is that you have to be a believer, not just a Christian according to the letter of the law. Naturally he chose Catholicism for his church, presumably knowing that the Catholic church (overtly) places higher value on correct action over correct belief. This stance led to the Protestant Reformation, so, as an ordained Calvinist minister, you know what I think of von Neumann’s “conversion.” On the other hand, I don’t see it as a great sin.  If it brought him peace at the time of his death, it was worth it. As far as I am concerned, dogma, whether it be Catholic or Protestant, is worthless.

Von Neumann was born Neumann János Lajos to a wealthy, acculturated and non-observant Jewish family. His Hebrew name was Yonah. Von Neumann was born in Budapest, then in the kingdom of Hungary, part of the Austro-Hungarian Empire. His father, Neumann Miksa (English: Max Neumann) was a banker, who held a doctorate in law. He had moved to Budapest from Pécs at the end of the 1880s. In 1913, his father was elevated to the nobility for his service to the Austro-Hungarian Empire by Emperor Franz Joseph. The Neumann family thus acquired the hereditary appellation Margittai, meaning from Marghita (even though the family had no connection with the town). János became Margittai Neumann János (John Neumann of Marghita), which he later changed to the German Johann von Neumann.

Von Neumann was a child prodigy. As a 6 year old, he could divide two 8-digit numbers in his head, and, reputedly, could converse in ancient Greek. Formal schooling did not start in Hungary until the age of 10. Instead, governesses taught von Neumann, his brothers and his cousins. His father believed that knowledge of languages other than Hungarian was essential, so the children were tutored in English, French, German and Italian. By the age of 8, von Neumann was familiar with differential and integral calculus, but he was particularly interested in history, reading his way through Wilhelm Oncken’s 46-volume Allgemeine Geschichte in Einzeldarstellungen.

Von Neumann entered the Lutheran Fasori Evangelikus Gimnázium in 1911. This was one of the best schools in Budapest, part of a specialized education system designed for the elite. The school system produced a generation noted for intellectual achievement, that included Theodore von Kármán (b. 1881), George de Hevesy (b. 1885), Leó Szilárd (b. 1898), Dennis Gabor (b. 1900), Eugene Wigner (b. 1902), Edward Teller (b. 1908), and Paul Erdős (b. 1913). Collectively, they were sometimes known as Martians. Wigner was a year ahead of von Neumann at the Lutheran School. When asked why the Hungary of his generation had produced so many geniuses, Wigner, who won the Nobel Prize in Physics in 1963, replied that von Neumann was the only genius.

Although his father insisted von Neumann attend school at the grade level appropriate to his age, he agreed to hire private tutors to give him advanced instruction in those areas in which he had displayed an aptitude. At the age of 15, he began to study advanced calculus under the renowned analyst Gábor Szegő. On their first meeting, Szegő was so astounded with the boy’s mathematical talent that he was brought to tears. By the age of 19, von Neumann had published two major mathematical papers, the second of which gave the modern definition of ordinal numbers, which superseded Georg Cantor’s definition. Von Neumann entered Pázmány Péter University in Budapest, as a Ph.D. candidate in mathematics in 1923, even though his father tried to steer him towards chemical engineering as a more profitable career. For his doctoral thesis, he chose to produce an axiomatization of Cantor’s set theory. He passed his final examinations for his Ph.D. in 1926 and then went to the University of Göttingen on a grant from the Rockefeller Foundation to study mathematics under David Hilbert. He completed his habilitation on December 13, 1927, and he started his lectures as a privatdozent at the University of Berlin in 1928, being the youngest person (24 years old) ever elected privatdozent in its history in any subject. By the end of 1927, von Neumann had published 12 major papers in mathematics, and by the end of 1929, 32 papers, at a rate of nearly one major paper per month. In 1929, he briefly became a privatdozent at the University of Hamburg, where the prospects of becoming a tenured lecturer were better, but in October of that year a better offer presented itself when he was invited to Princeton University in Princeton, New Jersey. In 1933, he was offered a lifetime professorship on the faculty of the Institute for Advanced Study in Princeton, which is separate from the university, and had been founded 3 years earlier. He remained a mathematics professor there until his death.

Von Neumann’s personal values are pretty much an open book. He liked to eat and drink, and his second wife, Klara, said that “he could count everything except calories”. He enjoyed Yiddish and crude humor (especially limericks). He was a non-smoker. At Princeton he received complaints for regularly playing extremely loud German march music on his gramophone, which distracted those in neighboring offices, including Albert Einstein, from their work. Von Neumann did some of his best work in noisy, chaotic environments, and once admonished his wife for preparing a quiet study for him to work in. He never used it, preferring the couple’s living room with its television playing loudly. Despite being a notoriously bad driver, he nonetheless enjoyed driving—frequently while reading a book—occasioning numerous arrests, as well as accidents. When Cuthbert Hurd hired him as a consultant to IBM, Hurd often quietly paid the fines for his traffic tickets. Von Neumann once said,

I was proceeding down the road. The trees on the right were passing me in orderly fashion at 60 miles per hour. Suddenly one of them stepped in my path.

The paradox that intrigues me concerns his work on the Manhattan project. He was called in, for several weeks at a time, to help solve the problem of getting the fissionable material in a nuclear bomb to explode. Without von Neumann’s equations on implosion it is unlikely that the Manhattan project would have been successful, certainly not at the rate that it was. Without getting too technical the problem is fairly easy to state simplistically. To get fissionable material to set off an explosive chain reaction it has to be of a certain shape, mass, and density. Von Neumann worked on the concept of an explosive lens that, via conventional explosives, would cause the fissionable material to implode, forcing it into a compact spherical shape that would trigger a nuclear explosion.  As best as I can tell, von Neumann saw this as a technical problem, and was not particularly concerned about the lives that would be lost should the bomb be detonated. Indeed, he was present at several experimental explosions set off in the New Mexico desert, and it seems likely that his exposure to radioactive material is what caused the cancer that killed him.

After the war he became what many see as the prototype for Dr Strangelove in that he advocated stockpiling nuclear weapons in the arms race to create what he called Mutually Assured Destruction (MAD) between the Soviet Union and the United States. His reasoning was that MAD, through stockpiling weapons, would guarantee that they would not be used, rather than the opposite. No rational leader would initiate a first strike if the result would be not just the destruction of the other party, but one’s own destruction also. This reasoning is based, in part, on game theory (which he created), and assumes that the participants in the “game” are rational. That might have been true in von Neumann’s time, but I’m not sure about now. Not least, there are many more countries stockpiling nuclear weapons these days, so the “game” has become considerably more complex.

In 1955, von Neumann was diagnosed with what was either bone or pancreatic cancer. He was not able to accept the proximity of his own death very well, and he invited a Roman Catholic priest, Father Anselm Strittmatter, O.S.B., to visit him for consultation. Von Neumann reportedly said, “So long as there is the possibility of eternal damnation for nonbelievers it is more logical to be a believer at the end,” essentially saying that Pascal had a point. Father Strittmatter administered the last rites to him. On his deathbed, Von Neumann entertained his brother by reciting, by heart and word-for-word, the first few lines of each page of Goethe’s Faust. He died at age 53 on February 8, 1957, at the Walter Reed Army Medical Center in Washington, D.C., under military security lest he reveal military secrets while heavily medicated.

Von Neumann’s wife noted: “He likes sweets and rich dishes, preferably with a good nourishing sauce, based on cream.  He loves Mexican food.  When he was stationed at Los Alamos… he would drive 120 miles to dine at a favorite Mexican restaurant.” This gives you a lot of options to celebrate the man, but I’ll go with pollo a la crema, a classic Mexican dish. You’ll need crema Mexicana, but if you cannot find it, use a mix of half and half heavy cream and sour cream. Crema Mexicana is a cultured cream with a sour, tangy taste, used in sauces.

Pollo a la Crema


1 tbsp olive oil
2 boneless chicken breasts, cut into strips
1 onion, peeled and sliced
½ cup fresh mushrooms, sliced
½ cup green pepper, seeded and cut into strips
½ tbsp Spanish paprika
½ cup rich chicken stock
1 cup crema Mexicana


Heat the olive oil in large skillet over medium heat. Sauté the chicken strips, peppers and onion until the chicken is cooked on the outside and the onions and peppers are soft. Add the cream, mushrooms, paprika and chicken stock. Bring to a boil, uncovered, and simmer for about 5 minutes, or the chicken is tender. Do not overcook. The sauce may be a little thin, but it should be creamy.

Serve hot immediately with refried beans, rice, and flour tortillas.

Aug 062017

On this date in 1945 the USA dropped the first of 2 atomic bombs on Japan. The first was on Hiroshima, the second, on August 9th, was on Nagasaki. Because Hiroshima was the first (and arguably the most popularly known) attack, it is the one commemorated in Japan and elsewhere on this date to remember the bombings in general. I will say a few things about the actual attack, but I won’t go into much detail because there is a mountain of information on it you can find. The bulk of my post concerns the ethics of the attack, followed by a classic Hiroshima recipe. My principal concern is the (mostly) modern concept of “total war” – warfare in which all enemy targets are fair game. As always, I’ll state my biases up front. For me, all warfare is hideous. Like Bertrand Russell, however, I do recognize the inherent ethical dilemmas raised by the Axis powers in the Second World War. Both the Germans and Japanese were engaged in ruthless genocide with a view to world domination by force, so it’s not ethically possible to simply state, “I refuse to play.” That would have led to the enslavement or murder of countless millions of innocent people. Nonetheless, one may still ask whether the tactics of the Allies in defeating such an atrocity were the best.

In the final year of the war, the Allies prepared for what was anticipated to be a very costly invasion of the Japanese mainland. This was preceded by a U.S. conventional and firebombing campaign that destroyed 67 Japanese cities. The war in Europe had concluded when Nazi Germany signed its instrument of surrender on May 8, 1945. The Japanese, facing the same fate, refused to accept the Allies’ demands for unconditional surrender and the Pacific War continued. The Allies called for the unconditional surrender of the Japanese armed forces in the Potsdam Declaration on July 26, 1945—the alternative being “prompt and utter destruction”. The Japanese response to this ultimatum was to ignore it.

By August 1945, the Allies’ Manhattan Project had produced two types of atomic bombs, and the 509th Composite Group of the United States Army Air Forces (USAAF) was equipped with the specialized Silverplate version of the Boeing B-29 Superfortress that could deliver them from Tinian in the Mariana Islands. Orders for atomic bombs to be used on four Japanese cities were issued on July 25. On August 6th the U.S. dropped a uranium gun-type (Little Boy) bomb on Hiroshima, and Harry Truman called for Japan’s surrender, warning it to “expect a rain of ruin from the air, the like of which has never been seen on this earth.” The Japanese continued to ignore the ultimatum so 3 days later, on August 9, a plutonium implosion-type (Fat Man) bomb was dropped on Nagasaki. Within the first two to four months following the bombings, the acute effects of the atomic bombings had killed 90,000–146,000 people in Hiroshima and 39,000–80,000 in Nagasaki; roughly half of the deaths in each city occurred on the first day. During the following months, the remainder of the deaths occurred from the effects of burns, radiation sickness, and other injuries, compounded by illness and malnutrition. In both cities, most of the dead were civilians, although Hiroshima had a sizable military garrison.

In April 1945 a Target Committee of generals and Manhattan Projects was formed to determine where the bombs were to be dropped if the Japanese failed to surrender.The Target Committee nominated five targets: Kokura, the site of one of Japan’s largest munitions plants; Hiroshima, an embarkation port and industrial center that was the site of a major military headquarters; Yokohama, an urban center for aircraft manufacture, machine tools, docks, electrical equipment and oil refineries; Niigata, a port with industrial facilities including steel and aluminum plants and an oil refinery; and Kyoto, a major industrial center. The target selection was subject to the following criteria:

The target was larger than 3 mi (4.8 km) in diameter and was an important target in a large urban area.

The blast would create effective damage.

The target was unlikely to be under air or ground attack by August 1945.

These cities were largely untouched during the nightly bombing raids and the Army Air Forces agreed to leave them off the target list so accurate assessment of the weapon could be made. Hiroshima was described as

an important army depot and port of embarkation in the middle of an urban industrial area. It is a good radar target and it is such a size that a large part of the city could be extensively damaged. There are adjacent hills which are likely to produce a focusing effect which would considerably increase the blast damage. Due to rivers it is not a good incendiary target.

The Target Committee wrote that:

It was agreed that psychological factors in the target selection were of great importance. Two aspects of this are (1) obtaining the greatest psychological effect against Japan and (2) making the initial use sufficiently spectacular for the importance of the weapon to be internationally recognized when publicity on it is released. Kyoto had the advantage of being an important center for military industry, as well an intellectual center and hence a population better able to appreciate the significance of the weapon. The Emperor’s palace in Tokyo has a greater fame than any other target but is of least strategic value.

Edwin O. Reischauer, a Japan expert for the U.S. Army Intelligence Service, was incorrectly said to have prevented the bombing of Kyoto. In his autobiography, Reischauer specifically refuted this claim:

The only person deserving credit for saving Kyoto from destruction is Henry L. Stimson, the Secretary of War at the time, who had known and admired Kyoto ever since his honeymoon there several decades earlier.

On May 30, Stimson asked the chair of the Target Committee (gen. Groves) to remove Kyoto from the target list due to its historical, religious and cultural significance, but Groves pointed to its military and industrial significance. Stimson then approached Truman about the matter. Truman agreed with Stimson, and Kyoto was temporarily removed from the target list. Groves attempted to restore Kyoto to the target list in July, but Stimson remained adamant. On July 25, Nagasaki was put on the target list in place of Kyoto.

I have long wondered why the bomb was not first dropped in an unpopulated area to demonstrate its effects but to spare civilian lives, and will note that this idea was considered and rejected. In early May 1945, the Interim Committee was created by Stimson at the urging of leaders of the Manhattan Project, and with the approval of Truman, to advise on matters pertaining to nuclear energy. Members of the Manhattan Project had serious moral qualms about using the weapon they had developed, and such qualms have led to no end of debate about the ethical dilemmas facing scientists ever since. During the meetings on May 31st and June 1st physicist Ernest Lawrence had suggested giving the Japanese a non-combat demonstration. Arthur Compton later recalled that:

It was evident that everyone would suspect trickery. If a bomb were exploded in Japan with previous notice, the Japanese air power was still adequate to give serious interference. An atomic bomb was an intricate device, still in the developmental stage. Its operation would be far from routine. If during the final adjustments of the bomb the Japanese defenders should attack, a faulty move might easily result in some kind of failure. Such an end to an advertised demonstration of power would be much worse than if the attempt had not been made. It was now evident that when the time came for the bombs to be used we should have only one of them available, followed afterwards by others at all-too-long intervals. We could not afford the chance that one of them might be a dud. If the test were made on some neutral territory, it was hard to believe that Japan’s determined and fanatical military men would be impressed. If such an open test were made first and failed to bring surrender, the chance would be gone to give the shock of surprise that proved so effective. On the contrary, it would make the Japanese ready to interfere with an atomic attack if they could. Though the possibility of a demonstration that would not destroy human lives was attractive, no one could suggest a way in which it could be made so convincing that it would be likely to stop the war.

The possibility of a demonstration was raised again in the Franck Report issued by physicist James Franck on June 11 and the Scientific Advisory Panel rejected his report on June 16, saying that “we can propose no technical demonstration likely to bring an end to the war; we see no acceptable alternative to direct military use.” Franck then took the report to Washington, D.C., where the Interim Committee met on June 21 to re-examine its earlier conclusions; but it reaffirmed that there was no alternative to the use of the bomb on a military target.

Like Compton, many U.S. officials and scientists argued that a demonstration would sacrifice the shock value of the atomic attack, and the Japanese could deny the atomic bomb was lethal, making the mission less likely to produce surrender. Allied prisoners of war might be moved to the demonstration site and be killed by the bomb. They also worried that the bomb might be a dud since the Trinity test was of a stationary device, not an air-dropped bomb. In addition, only two bombs would be available at the start of August, although more were in production, and they cost billions of dollars, so using one for a demonstration would be expensive.

Here I’ll leave you to sort out the ethical problem for yourself.  A look at a map of territory still under Japanese control by August 1945 shows that, while the Allies were definitely winning and would eventually succeed, a hard slog was still to come and the Japanese would never surrender using conventional weapons until the mainland was completely overrun by the Allies. This could have taken years. As it is, pockets of Japanese forces, still fighting after the surrender was signed, sporadically showed up in the Pacific for decades.

Truman’s and Churchill’s equation was brutal, yet simple. One way or another the Allies will win, but lives will be lost in the process. How many lives, and whose lives were the key questions – Allied military lives (and Japanese military) versus Japanese civilians?  This brings up the issue of “total war.”  Throughout much of the modern era, and certainly since the Geneva Conventions following the First World War, there had been a sense in the West that civilians and civilian targets were off limits in warfare. But there is also no question that throughout Western history from ancient times forward, total war, that is war in which no one was safe, military or civilian, was the norm. Romans, Greeks, Persians, Assyrians, Babylonians etc. in ancient times routinely slaughtered or enslaved ALL the inhabitants of conquered lands utterly laying waste to towns and farm lands, and looting all their treasures.  Total war is not a modern invention. Still, in modern times, particularly in the 20th century in the aftermath of the atrocities of the First World War, there was a growing sense that civilians should never be targets of war. During the Napoleonic Wars civilians routinely watched battles from a safe distance, sometimes bringing picnics as part of enjoying the spectacle and safe in the knowledge that they would not be involved. Modern weaponry shattered this state of affairs, and the ideological and cultural animus of the belligerents in the Second World War was absolute.

The US had no hesitation in sending people of Japanese origin to internment camps even though they were (mostly) US citizens, many of whom were born in the United States. There was a sense (not universal) that their loyalties would be with Japan and their existence on US soil was a threat. The Allies carpet bombed cities such as Dresden just as the Axis powers rained down death and destruction on cities in England. Nuclear bombs were, therefore, nothing more than an extension of this policy with one bomb taking the place of tens of thousands. In that context I do not believe that there are easy answers, and I’m not going to give one. I will say, though, that the world is different now because of Hiroshima and the events that followed, including the Cold War. Total war has become the norm; no one is safe. These are times that I hope will be roundly condemned by future generations – but I have my doubts.

Hiroshima is known for okonomiyaki, a savory pancake cooked on an iron griddle, usually in front of the customer. It is cooked with various ingredients, which are layered rather than mixed together as done with the Osaka version of okonomiyaki. The layers are typically egg, cabbage, bean sprouts (moyashi), sliced pork/bacon with optional items (mayonnaise, fried squid, octopus, cheese, mochi, kimchi, etc.), and noodles (soba, udon) topped with another layer of egg and a generous dollop of okonomiyaki sauce (Carp and Otafuku are two popular brands). The amount of cabbage used is usually 3 to 4 times the amount used in the Osaka style. It starts out piled very high and is generally pushed down as the cabbage cooks. The order of the layers may vary slightly depending on the chef’s style and preference, and ingredients will vary depending on the preference of the customer. Okonomiyaki (お好み焼き o-konomi-yaki)  is derived from the word okonomi, meaning “how you like” or “what you like” and yaki meaning “grill” (as in yakitori and yakisoba). Okonomiyaki is cooked in different ways in various parts of Japan including Osaka, Kansai, and Tokyo. The Hiroshima style is of special importance.

As is my custom, I’m not going to give you a recipe because you won’t be able to replicate this dish at home both because of the need for specific ingredients and for certain cooking skills and equipment.  The Japanese don’t make it at home.  Here’s a video instead: