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Volume 14: Game Theory and the Nuclear Age

The Klein Bottle

Destroyer of Worlds

“It is a harnessing of the basic power of the universe. The force from which the sun draws its power has been loosed against those who brought war to the Far East.” – Harry S. Truman


Imagine wanting to know what is on the inside of a baseball. But you aren’t allowed to cut into it or peel off the skin. You can’t look for interactions with acid, fire or any other substance. Your only choice is to stand a great distance away, shoot at it with a pistol, and see what flies off. That is nuclear physics.

As late as the year 1895, there was very little evidence of any particles smaller than the atom. A mere fifty years later, the power of these sub-atomic particles had been harnessed in the most dramatic fashion possible. The unleashing of the nuclear age changed the rules of war: mankind now had the power to destroy itself. Two superpowers soon would face off in a five-decade struggle, the likes of which had never before been seen. To survive, our greatest minds had to develop a new way of thinking about the very nature of cooperation and competition.

  • How do nuclear bombs work? How were they built?

  • How did nuclear weapons proliferate?

  • What is game theory?


A word of caution from the author:

Nuclear weapons are terrible things. This is true in all of the word’s meanings.(1) Terrible: extremely bad, as in “a terrible movie.” Terrible: formidable in nature, as in “a terrible responsibility.” Terrible: extreme or great, as in “a terrible disappointment.” Nuclear weapons are not to be trifled with, joked about or handled except with extreme care.

Which is all to say – this Volume will prominently feature death, destruction, fallout, nuclear winters and the end of the human race. We will flippantly talk about the gruesome deaths of millions and even billions. We will explicitly do this through the lens of a game, winning and losing, keeping score of the destruction. We will not modify our usual style of writing or the ongoing attempts at mild humor. We are not focused on the morality of these weapons, their development or their use. Except in the paragraphs immediately following.

The previous five hundred years have been a period of steady human advancement with no major steps back. It was inevitable that we would learn about the power of the atom. Every man, woman and child is innately aware of this power. It stares you in the face every day, from sunrise to sunset. We were going to learn about radioactivity, fission and fusion and chain reactions. It necessarily follows that we would try to harness this power. Even with knowledge of their destructive potential, we were eventually going to develop nuclear weapons capabilities. They are a by-product of these five centuries of discoveries about the Universe we live in.

Morality comes only after development: how can these weapons be controlled to prevent their use? The two decades after the Trinity Test were not just a scramble to build bigger bombs, but also to develop these controls. Game theory contains the most effective controls we’ve found. And we can only learn the game theory of nuclear weapons by repeatedly simulating the destruction of the world.

Only by understanding these weapons can we prevent their use.



How do nuclear bombs work? How were they built?

The three primary sub-atomic particles were discovered by three citizens of the British Empire over a period of thirty-five years around the turn of the century.(2) All three were associated with the famed Cavendish Laboratory at Cambridge University.(3)

In 1897, J.J. Thompson found that cathode rays travel too fast for particles as large as an atom. This meant that there must be at least one smaller, more fundamental particle. He also found that these rays interact with an electrical field; this implied that the particle he discovered has a negative charge. Thompson had discovered the electron.

By 1908, Ernest Rutherford had already won a Nobel Prize for formalizing the nature of radioactivity. One day, he decided to shoot “alpha particles” at a sheet of gold foil. Some of the alphas bounced back. As Rutherford himself said, “It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.” Clearly, there were some tiny, dense parts in the atoms making up the gold foil. Because they deflected positively-charged alphas, they must themselves have positive charge. Rutherford named these particles protons.

Scientists theorized that something was still missing. Atoms were heavier than expected, so something else had to be there. These theoretical particles had to be uncharged, which would make them more difficult to find. James Chadwick worked tirelessly, irradiating various substances, developed new detection techniques, and found the elusive neutrons. The basic model of the atom was complete: a nucleus of tightly bound protons and neutrons with tiny electrons orbiting.(4)

The Bohr Model

High school chemistry is the study of electrons; chemical reactions involve exchanging or sharing them in some manner. Radioactivity is the study of the nucleus: protons and neutrons. For instance, if you bombard an atom with neutrons, some of these will be captured by the nucleus. As the nucleus grows, the atom becomes less stable. If it gets too far, an atom may undergo Beta decay, where a neutron turns into proton and an electron. Your atom is now a different element, but the nucleus is the same size.(5) Depending on the isotope, an atom may also undergo Alpha decay, spitting out two protons and two neutrons. This will make our atom into a lighter element. Because they have no charge, neutrons are the best particle to use in nuclear reactions. With Chadwick’s discovery, scientists could start to have some real fun.(6)

In 1934, Enrico Fermi bombarded the heaviest naturally occurring element, Uranium, with neutrons. He hoped to synthesize heavier elements, never before seen by man. Soon, he had created two elements that were not Uranium; he believed he had synthesized the elements that later became known as Neptunium and Plutonium. But Otto Hahn, Lise Meitner, Otto Frisch and Fritz Strassman, conducting similar experiments, soon identified one of these elements as Barium, a much smaller element. Rather than going through methods like Alpha or Beta decay, the Uranium nucleus had been cleaved in two. They had discovered nuclear fission.

There was a big problem with fission; it created a large amount of energy with no obvious source. It could come from only one place: the masses of the “children” of the fission reaction, added together, was less than that of the “parent”. We know from Albert Einstein that E = mc2. The “m” is mass and “c” is the speed of light, a very large number. The small decrease in mass during fission accounts for the enormous amount of energy created.


An Aside: Nuclear Binding Energy Calculations

It sounds boring, but I assure you it’s quite explosive. Nuclear binding energy is how tightly an atom’s nucleus is held together. Because energy and mass are equivalent, the binding energy of an atom is equivalent to its mass defect: how much less the atom weighs than the sum of its parts. The greater the mass defect, the more stable and less radioactive an atom is.

One of the most common fission reactions involves Uranium getting hit by a neutron, splitting into Rubidium and Cesium and releasing two neutrons:

U + n -> Rb + Cs + 2n

Looking up the masses of these atoms, we see that for each fission reaction, 0.323 * 10-27 kg has been converted to energy. Multiplying by c2 shows this reaction creates 2.9*10-11 Joules of energy. A tiny amount – but this is for each individual atom.

There are 6.022*1023 atoms in a mole; a mole of Uranium-235 has a mass of 235 grams. This is about half a pound of Uranium, it would fit easily in a tablespoon.

If you could create a chain fission reaction for this amount of Uranium, it would release 1.75*1013 Joules of energy. In other words, you can fit enough Uranium in the palm of your hand to provide for your family’s annual energy usage.


Leo Szilard, a Hungarian-born physicist, had already thought about the possibility of nuclear chain reactions. In the newly discovered fission reaction, each atom releases three neutrons when it splits.(7) If these neutrons “hit” other Uranium atoms and cause more fission, each of these atoms would in turn release three neutrons. The number of fission reactions would increase to an incredible rate. Incredible rate of reaction, enormous amount of energy. This is a bomb. Szilard, a Hungarian who emigrated to America to avoid the Nazis, explained the possibility to Einstein, who was equally concerned. Einstein added his imprimatur to a letter to FDR, explaining the significance of nuclear chain reactions. Intelligence showed that Nazi Germany might be developing nuclear technology. The United States soon committed its enormous industrial capacity to the development of a nuclear weapon.

The first step towards building The Bomb was to demonstrate a chain reaction. Working on a squash court under the stands of the University of Chicago football stadium, a team led by Enrico Fermi first “went critical” on December 2, 1942.(8) The biggest challenge was production of Uranium-235 and Plutonium, which would fuel the Bomb. The Army acquired enormous sites at Oak Ridge, Tennessee and Hanford, Washington to do this. In general, to create a Bomb, two smaller, sub-critical, amounts of nuclear fuel must be combined to make a critical mass – very quickly. To solve this and other technical problems, a group of top scientists moved to Los Alamos, high in the New Mexico Desert. The scientific work was placed under the control of Robert Oppenheimer, the Father of the Bomb. Together with many other sites, this was the Manhattan Project.

While work was proceeding on a fission bomb, scientists also recognized the potential for a bomb based on joining atoms together, or fusion. Fusion is what the sun does: Hydrogen atoms combine to form Helium. This reaction causes a much greater loss of mass than Uranium fission, with the attendant greater release of energy.(9) But, to cause a fusion reaction you need to heat your fuel to a very high temperature. The best way to do this? Set off a Fission Bomb. At the time, the Fusion Bomb was called The Super; today, we usually say H-Bomb, after Hydrogen’s chemical symbol.(10)

How did nuclear weapons proliferate?

All of the scientists who worked on the first nuclear weapons had a keen understanding that they would change the world. They understood long before the politicians exactly what it meant to unleash the power of uncontrolled nuclear chain reactions. Winston Churchill, for all of his greatness, thought The Bomb was just another weapon. Giv