by Peter Byrne
Nestled inside the last few pages of Nancy’s Princeton diary is a carefully torn newspaper clipping, a few paragraphs from a literary review of a book about Lucrezia Borgia, the 15th century femme fatale, daughter of a Pope, suspected murderess:
‘Even as a woman,’ writes Miss Haslip, she ‘retained a curious look of immaturity,’ the look of one from whom ‘you would not expect a strict moral standpoint or an irrevocable decision,’ a person ‘with whom everything was soft and pliable, [whose] very nature was fluid, flowing with the tide, accepting with a smile whatever life had to offer.’
In other words, a woman so lacking in definition that she would have attracted no more than passing notice had it not been for the extraordinary background against which she played a part.
And it is in this curious image of the wall-flower cum poisoner, Lucrezia Borgia, that Nancy, who was to became obscured by Everett’s shadow, once saw her own reflection.
BOOK 2
GAME WORLD
5 Demigods
There is a tendency to forget that all science is bound up with human culture in general, and that scientific findings, even those which at the moment appear the most advanced and esoteric and difficult to grasp, are meaningless outside their cultural context.
Edwin Schrödinger, 19521
Shortly before the start of the fall term of 1953, Everett arrived in Princeton driving a Buick loaded with an automatic transmission (a luxury item in those days). Eyes of grey, he was five feet, nine inches tall and trim at 155 pounds. His red-brown hair was slightly receding, worn slicked back. Parking at the Graduate College, he lugged his possessions to the top floor of the residence hall, which resembled a gentlemen’s club. Everett and his British roommate each had a tiny bedroom; they shared a bath, and a living room with a fireplace. The basement sported bowling alleys, ping pong tables, pool tables, a television, and an ice machine.
Established in 1746, Princeton’s neo-Gothic architecture was patterned on the gargoyle-studded buildings at the British universities, Oxford and Cambridge. Cultural traditions were also imported. Black, floor-length gowns were worn to dinner in oak-paneled Proctor Hall under a stain glass window representing the “Light of the World Illuminating the Seven Liberal Arts of Christian Learning.” Tipping the housemen, waitresses, kitchen help, and gardeners was forbidden, because, according to the student handbook, that biased the servants toward wealthy students.2
The economic and social life of Princeton town revolved around the Ivy League university, the headquarters of Educational Testing Services, a Radio Corporation of America research lab, and the internationally renowned Institute for Advanced Study. Princeton was a major center of revolutionary work in the physical sciences, attracting gown-wearing geniuses to settle in the bucolic town. In the early 1930s, the Institute’s star catch, Einstein, described Princeton as, “A quaint, ceremonious village of puny demigods on stilts.”3 But in the neon glare of post-war consumerism, as the academy allied with the national security apparatus and weapons manufacturers, many a demigod exchanged gown for business suit.
Tea time for brainiacs
The Institute for Advanced Study was founded by the millionaire owner of Bamberger’s department stores in 1930. It supports theoretical work in history, public policy, mathematics, physics, economics, and information theory. For many years, it was the intellectual home of Einstein and John von Neumann, both of whom profoundly influenced Everett’s intellectual development. It was also a fount of operations research. In 1952, the Institute fired up the first of the “Princeton-class” computers, digital machines built to von Neumann’s specifications with military funding, and installed at the Los Alamos, Oak Ridge, and Argonne National Laboratories, as well as at the RAND Corporation, an Air Force “think-tank” based in Santa Monica, California.4
The Los Alamos computer (acronym: MANIAC) cut its baby teeth crunching numbers for the hydrogen bomb project.5
Although the Institute was not formally affiliated with the university, it’s woody campus was within walking distance. Its faculty mixed easily and often with their college-based counterparts, attending afternoon teas sponsored by Princeton’s mathematics department in Fine Hall. Said Oppenheimer of the teas: “It is where we explain to each other what we don’t understand.”6 Chatting informally, professors and students discussed the logic of economics and warfare in ways that rippled out into the world. Everett was a regular at the teas.
In his first year at Princeton, Everett attended weekly game theory seminars at Fine Hall led by Albert Tucker and Harold Kuhn. The two professors also organized a series of formal game theory conferences featuring the illuminati of game theory: von Neumann; Princeton professor of economics Oskar Morgenstern; Massachusetts Institute of Technology (MIT)’s John Forbes Nash; and RAND’s star gamer, Lloyd S. Shapley. At one of these conferences, Everett presented a paper on military tactics, “Recursive Games,” which is considered a classic in the annals of game theory.
In its early days, game theory was intended to provide rational solutions to problems in economics, sociology, and military planning. But as the shadow of McCarthyism darkened the halls of academia, the game-playing habitués of Fine Hall quickly learned that dissenting from political agendas (however irrational) came with a price. Shortly after Everett arrived in town, the Institute’s director, Oppenheimer, was publicly disgraced by the board of the Atomic Energy Commission. Oppenheimer had been the scientific leader of the Manhattan Project, but, after Hiroshima, he openly opposed developing a hydrogen bomb. In retaliation, the commission stripped him of his security clearance. The spurious reason given for the discipline was that in his youth, Oppenheimer had leaned to the left ideologically, and was now (although not when these matters were reviewed prior to his hiring by the Manhattan Project), “susceptible to influence” and, therefore, unreliable.7
In the wake of political persecution, Oppenheimer kept his job; unlike Princeton assistant professor David Bohm, a stellar quantum theorist, whose academic career was derailed by McCarthyism (and, to a lesser extent, by his renunciation of the prevailing interpretation of quantum mechanics).
Memory lane
During the first semester, Everett made three good friends among his classmates. Charles Misner was his sounding board as he worked up his interpretation of quantum mechanics during their second year in grad school; they remained friends until Everett died a quarter century later. Hale Trotter ended up chairing the mathematics department at Princeton. And Harvey Arnold retired from academia after teaching statistics for many years at Oakland University in Rochester, Michigan. In 2007, the three men, then in their late seventies, got together to reminisce about Everett.8
The four classmates met regularly for cocktails before dinner. Everett was fond of cherry herring, a cheap, sugary liquor that packs a wallop. And he had a collection of hard liquor in his room, mostly purloined from his father’s liquor cabinet. Arnold, Trotter, and Misner liked traipsing upstairs to Everett’s room with a bucket of ice from the basement. He poured them nightcaps from an odd bottle with four spouts, each spout tapping a different liquor.
TROTTER:
Everett was a lot of fun. He enjoyed needling people.
MISNER:
But always in good humor.
ARNOLD:
He was very competitive at whatever it was, if it was a poker game or it was ping pong.
MISNER:
But it was always friendly competition.
ARNOLD:
But he always wanted to go away the winner and he would make you stay there until he succeeded which didn’t usually take that long with me. But if I’d win one he’d say, ‘We’re playing another game!’ And it surprised me after I got to know him that he was as brilliant as he was. It didn’t come across until you got close to him. And then you would recognize that this guy would be on top of the world. He was smart in a very broad way. I mean, to go from chemical engineering to mathematics to physics and spending most of the time buried in a sc
ience fiction book, I mean, this is talent.
The men toasted their departed friend with a glass of sherry.
TROTTER:
Everett’s father visited Princeton once, briefly. He let it out that within the family Hugh was called ‘Pudge.’ Hugh was not pleased.
During their third year of grad school, the four shared an off-campus apartment. Everett liked to gorge, especially on steak. That was the year he met Nancy Gore. “She was a delightful, outgoing, pleasant person,” Arnold recalled.
Probability is everywhere
Physics graduate students were expected to be self-starters. Professors did not take class attendance, nor issue grades. Students were required to pass their “general examinations” at the end of the second year (equivalent to a Masters degree), and then to write a doctoral thesis.
During his first semester, Everett took a course in electro-magnetism, a seminar in algebra, and Introductory Quantum Mechanics, with Robert H. Dicke, a model of the scientist-businessman. During the Second World War, Dicke worked on radar at MIT’s “Rad Lab.” In the 1960s, he helped confirm the existence of the microwave background radiation, which is a lingering record of the state of the universe as it existed immediately after the Big Bang. He also did important work testing predictions about gravity made by Einstein’s theory of general relativity. Uniting theoretical and applied physics with information theory, he invented and marketed a type of amplifier (called a lock-in amplifier), which pulled coherent messages out of electronic jumbles of white noise.
Under Dicke’s tutelage, Everett studied John von Neumann’s classic text, Mathematical Foundations of Quantum Mechanics (1932), and David Bohm’s textbook, Quantum Theory (1951). As a student of quantum theory and, also, game theory, (both fields disciplined by the mathematical rigor of von Neumann), Everett was immersed in the mathematics of probability: that mysterious combination of information and belief that obeys formal laws. The science and art of measuring probability is embedded in most decision-making processes: from cooking to playing dice to making love or war. Probability quantifies risk; and probability is the principal tool wielded in game theory, quantum mechanics, and operations research.
The study of how people make decisions, or more bluntly, how people gamble for stakes, began in the mid 17th century in France. Blaise Pascal, Pierre de Fermat, and, later, Pierre-Simon Laplace were among those who discovered the axioms of the probability calculus, a method of adding and subtracting and multiplying ratios that gave birth to statistics, the study of data on behalf of the political state, hence the appellation.
In the latter part of the 19th century, James Clerk Maxwell and Ludwig Boltzman applied probabilistic methods to the microscopic world: constructing a statistical explanation of thermodynamics (i.e. laws that govern the transformation of energy from one form to another). They uncovered a dialectical relationship between entropy9 and probability, between microscopic systems and macroscopic systems. Much later, in the 1920s, probability was, surprisingly, found at the existential root of quantum physics.
Practitioners of quantum mechanics and game theory (and bookies!) make lists of possible events and rank them with odds. They chart directions in which the future may unfold based upon information—a history of the frequency of past occurrences—and the belief that future events are related to past events. There are, however, important differences between how the laws of probability pertain to the “classical”10 world, composed of macroscopic objects, and the quantum world, composed of elementary entities describable both as objects (particles) and probability waves.
In classical physics, reality is governed by deterministic laws, i.e. classical mechanics. The probability of accurately predicting an outcome in classical mechanics is a function of possessing information about inputs. For example, if we know the mass of our planet and the mass of our star and the distance between them, we can use gravitational formulas set down by Isaac Newton in the 17th century to predict the path of the Earth’s orbit around the Sun with close to 100 percent accuracy. In classical physics it was thought that an observer who possessed perfectly accurate information about the initial state of every object in the universe at a given instant, could, in theory, exactly predict the configurations of all future states of the universe. Of course, the universe is far too complex (and relativistic) for us to access that much simultaneous information, but, in theory, the motion of the classical, macroscopic world is predictable because its laws are determinist.
In classical mechanics—and game theory—the more information we have with which to calculate predictions, using the “relative frequency” with which certain outcomes have previously occurred, the less uncertainty we will have about a possible outcome in the future. Possessing information about the past allows us to hold a degree of belief that past relations will continue to prevail in the future. For instance, when heads emerges from a series of coin flips 50 percent of the time, it is reasonable to believe that this ratio will continue into the future. But for any single coin flip, we cannot know with any certainty that the coin will be heads, even if the last 100,000 flips have all been tails! All we can reasonably believe is that there is a 50 percent probability that it will be heads (or tails) each time the coin flips. It is often said that probability is a measure of ignorance (and ignorance is the opposite of information). So, the greater the information content (e.g. a record of the relative frequency of heads turning up in the past), the greater the predictive power of the probability calculus.
But there is no such thing as possessing (even in theory) perfectly accurate information about the properties of a quantum object at any given moment. Consider an electron: it has no identifiable position until we “measure” or interact with it. And knowing something definite about one property of an electron, such as its exact position in space, means that we cannot simultaneously and precisely know its momentum.11
Uncertainty rules the quantum world: an electron does not have a definite orbit around an atomic nucleus, rather, its path is smeared out inside a range of possible orbits, a “cloud,” which we know as a probability distribution.
It appeared to most physicists of Everett’s day that the quantum world was fundamentally indeterminist, although Everett was to disagree with that interpretation; his model of the quantum world is thoroughly determinist. He had no particular longing to live in a deterministic universe, he was simply following the logic of the standard equations. But before tackling the quantum question, he cut his probabilistic teeth on game theory, which is classically determinist.
6 Decisions, Decisions—the Theory of Games
Decisions made in the face of uncertainty pervade the life of every individual and organization…. Reasoning is commonly associated with logic, but it is obvious, as many have pointed out, that the implications of what is ordinarily called logic are meager indeed when uncertainty is to be faced…. [L]ogic alone is not a complete guide to life.
Leonard Savage, 19541
For millennia, soldiers have mirrored real life by playing military games. In the 19th century, Prussian generals played Kriegsspiel, a game that tested rules for maneuvers with chance occurrences, such as a surprise attack. At Princeton, Everett learned the military application of modern game theory directly from the academics who invented it; he absorbed that dark art into his personality.
The Theory of games was largely systematized by von Neumann, the Hungarian-born polymath. In 1928, he proved an important theorem showing that two players with completely opposed interests always have a rational strategy for playing a “zero-sum” game, defined as an outcome where one player’s gain mirrors the other player’s loss. In 1944, von Neumann and Morgenstern published Theory of Games and Economic Behavior. The massive, highly technical volume was the Book of Genesis for the game theory industry that rose out of the ashes of the Second World War on the back of operations research, defined as the application of statistics to warfare and other complex undertakings. Stating their goal, von Neumann and Morgens
tern wrote,
We wish to find the mathematically complete principles which define ‘rational behavior’ for the participants in a social economy, and to derive from them the general characteristics of that behavior.2
At its foundation, game theory posits the existence of rational players who make decisions based on the relationship between information, probability, and personal preferences, or “utilities.” Its efficacy, naturally, hinges on how one defines “rationality.” And, in von Neumann’s scheme, rationality is equated with the maximization of “expected utility”3 in a list of ranked preferences for a certain outcome.4
Although von Neumann and Morgenstern’s work targeted how profit-seeking individuals should act inside a capitalist economy, the mathematical techniques that they developed were quickly applied to optimizing choices in military tactics and strategy, including nuclear war planning.
Game theory calls for assuming that equally rational opponents will pick their optimum choices out of a finite set of possible strategies. The “pay-off” values are arrayed in matrices, i.e. intersecting rows and columns displaying the consequences for each player’s chosen strategy as dependent upon combining the decisions of the players.
