Literature and film absorbs meaning through what one might call reality vectors, slices of sunlight that illuminate the art. These vectors may not be literally “true”. However, they speak to us. When each book or movie is activated within a universe of reality vectors, higher truths unfold like flames.
In The Journal of Jeremiadus – some diversions aside – we have explored and tried to extend the concept of randomness as Nassim Nicholas Taleb presents it in his influential works, Fooled by Randomness, The Black Swan, and Anti-Fragile. I have described Taleb as a modern-day Jeremiah, one who speak inconvenient truths to masses of people who, by definition, will not hear. And so we have a simple understanding of a world in which God is absent, but sin is present.
Anyone interested in my previous essays on Taleb can read them here and here. In this present essay, I would like to shape Taleb’s ideas in relation to two reality vectors – the film Donnie Darko and the concept of “summing over histories” deduced by theoretical physicist Richard Feynman. As I indicate above, a reality vector does not have to be literally true. Donnie Darko is a story that never happened. Summing over histories represents a series of quantum events that violate every rule of traditional (non-particle) physics. As Feynman himself said about summing over histories, no rational explanation exists for this phenomenon that is scientific fact.
Both Donnie Darko and summing over histories attune us to a central proposition in Taleb’s writings, that stochastic processes, particularly randomness, rule reality. With his Monte Carlo generator, Taleb exposes the fraud that Wall Street bankers and traders can lay claim to any particular skill or insight to account for their accumulation of the wealth of Croesus. Their success is only one of thousands or millions of outcomes, fractions of a whole which sums all conceivable outcomes and their probabilities.
Let’s start with Donnie Darko. We will ignore the wormhole that allows Donnie to travel through time, the silliest part of the movie and the part that most egregiously toys with our emotions. We will instead focus on the two parallel events – the scene where the jet engine lands on the house and Donnie is not in his bedroom and the scene where the engine lands on his bedroom while he is lying in bed. And let’s focus on the entirely different narratives that unfold as a result – climaxing with the very touching scene at the end of the movie where Donnie’s girlfriend waves at the bereaved mother, carrying no knowledge of the mother or of her son beyond the tragedy she has witnessed.
In one version of the movie, which consumes most of the narrative, everything changes around Donnie – and he is an agent of most of this change – the flood, the fire, the girlfriend – but he does not change. In the other version, which captures the climax, everything around Donnie stays the same – no flood, no fire, no girlfriend – but Donnie does change. Most profoundly. He dies.
Donnie’s illness – schizophrenia – refracts his awareness throughout the movie that reality is unreal, precisely because it is not unique. This is a difficult, complex truth to live with, and it explains his hallucination about Frank the Bunny, who tells him the world will end in 28 days. However, the world – as the sum of all worlds – doesn’t end in 28 days, only Donnie, and only the world as he knows it perish.
This is the key point. We carry no knowledge of the other alternatives that exist among the full range of possible outcomes, depending only on the boundaries the range of outcomes. For this reason, we think we live in the only possible reality. Donnie’s awareness of multiple realities both tortures and excites him.
In Donnie Darko, Frank the Bunny serves as a kind of Jeremiah – he captures the mind of Donnie and uses him as instrument of destruction through fire and water. Frank visits a kind of random mayhem that explodes the conservative, manicured, Bush-voting, golf-playing, cult-following comfort of Donnie’s community. This apocalyptic mayhem both fuels and expresses Donnie’s seeking for some reality beyond what is “real” but also “fake” in his own community. When Donnie finds someone to love, it amplifies his will to break through the wall and escape into another history, with a different reality, one where he can serve love and not succumb to illness, but one that has no room for him.
Summing over Histories
To grasp the concept of summing over histories, let’s start with Brownian motion, the study – originating with Einstein’s least-known 1905 paper – that laid the foundation for particle theory and for various real-world models of complex crowd behavior and the sum of the distribution of outcomes within bounded environments, including financial markets. Brownian motion has been associated with stochastic processes, probability theory, and the random walk. Studies and experiments building on the concept of Brownian motion have led to new ideas about randomness, multiplicity, and simultaneous realities that inspire the work of Taleb.
Einstein extended the possibilities for the application of quantum concepts of probability to the physical and human world with his exploration of the concept of the half-life of atoms. The methods used to calculate atomic half-lives applied statistical theories that become the foundation of actuarial science and the modern business of insurance. Once again, Einstein began playing with the statistics and probabilities associated with atomic decay, assuming that eventually scientists would explain the patterns of atomic decay and abandon the crude statistical methods associated with actuarial science. “God does not play dice with the universe,” Einstein said. But no explanation has ever been found, and in the 1930s Schrodinger’s experiments with the double-slit method for determining whether light moves as particles or waves introduced the possibility of a systematic analysis of probability at the quantum level.
Theoretical physicist Richard Feynman blazed a path for physics in the post-war world, and his concept of summing over histories informs the work of Taleb, who in his typical freewheeling way, borrowed (and mangled) the term “summing under histories” from Feynman. In fact, Feynman rarely (never?) used the term “summing over histories”, although it is a felicitous expression. He called his concept of the simultaneity of multiple instances of the same moment in time the “path integral formulation”.
The path integral formulation of quantum mechanics replaces the classical notion of a single, unique trajectory for a system with a sum over an infinity of possible trajectories to compute a quantum amplitude. The basic idea of the path integral formulation can be traced back to Norbert Wiener. Feynman completed the method in 1948. Beyond its significance for establishing the symmetry between space and time, the path integral formulation also relates quantum and stochastic processes, which provided the basis for the grand synthesis of the 1970s unifying quantum field theory with statistical field theory. The path integral provides a method for summing up all possible random walks.
In a succinct statement for lay consumption, Cornell physics professor Tomas Alberto Arias uses three postulates to outline Feynman’s particular contribution to the path integral formulation: Events in nature are probabilistic. The probability for an event to occur is given by the square of the complex magnitude of a quantum amplitude for the event. The quantum amplitude associated with an event is the sum of the amplitudes associated with every history leading to the event.
The quantum amplitude associated with a given history is the product of the amplitudes associated with each fundamental process in the history. A fundamental process cannot be interrupted by another fundamental process. The fundamental processes therefore constitute indivisible “atomic units” of history. These individual histories may always be divided unambiguously into ordered sequences of fundamental events, which is the framework for computing the amplitudes of individual histories from fundamental processes.
According to Arias, the fact that the definition of fundamental processes is not very specific is actually one of the strongest aspects of the Feynman approach, as it can allow us to group fundamental processes together into larger units that make up new fundamental processes. This procedure is known as renormalization and is one the great central ideas in managing the infinities in quantum field theory.
To sum up: Particles do not have single histories and paths, as in classical physics. Instead, particles simultaneously track every imaginable path in space-time. When one calculates all trajectories, one can arrive, probabilistically, at the most likely path the particle traveled in its journey through space-time. Most recently, Stephen Hawking has extended quantum theories of space-time and the sum of histories to cosmological theories of universal origins and trajectories.
Taleb and Alternative Histories
It is not commonly known – outside the world of physicists – how closely related the study and application of probability and statistics are to theoretical physics. For years, from the 1980s until the great boom of 2008, physicists and mathematicians poured into hedge funds and securitization shops because their skills translated so directly into the work of the most cutting edge financial institutions. As Taleb enjoys telling us, many were Russian scientists and mathematicians (and chess players and pianists) pouring out of the former Soviet Union.
For this reason, it is useful to remember that Taleb also practiced mathematical finance professionally. He was one of “those PhDs”. Taleb wrote his doctoral thesis at the University of Paris on the mathematics of derivatives pricing. Presently, he advocates “stochastic tinkering” as a means of scientific exploration and discovery. In other words, when it comes to mathematics, Taleb is not a neophyte, and this knowledge provides all sorts of possibilities for adducing history, not (he is careful to say) from formal mathematical models, but from an inductive playfulness informed by a serious and deep understanding of mathematics. Let’s take a look, and then circle back to our “reality vectors” to see what light they shed on the thinking of Nassim Nicholas Taleb.
Oddly, the climactic moment of Taleb’s Fooled by Randomness, in a sense, comes early in the game, with his chapter entitled “A Bizarre Accounting Method.” In this chapter, Taleb introduces the idea of “alternative histories,” its premise being that judging historical outcomes requires that one consider the alternatives. These alternatives are commonly voiced by those who have “failed” (since those who are victorious assume by definition that the outcome is the direct result of their superiority, and so must be inevitable). Taleb spends some time using the example of Russian roulette to flesh out his understanding of probability, uncertainty, and multiple realities (ironically, in Russian roulette, the one who fails has no voice at all on the alternative outcomes).
Be that as it may.
In a single page, Taleb pulls together various threads of thought concerning alternative historical outcomes – all possible worlds (Leibniz), parallel universes (Saul Kripke), many-worlds (Hugh Everett), and scenario analysis(Arrow and Debreu). For Taleb, it is risk and uncertainty that skeins together these concepts, just as probability and uncertainty and randomness tie together outcomes in particle physics. Many worlds or what-if scenarios both depend on the philosophical ability to imagine time and reality, not as a single, linear passage, but as a series of probabilities, which exist as independent outcomes. One can flip a coin and have it turn up heads 10 times in a row. That is no guarantee the 11th time will also turn up heads. One can play Russian roulette and avoid the bullet hundreds of times. The patience and grace of God eventually wanes, however, and He eventually, tenderly deposits a bullet in the head of the fool. History is a trickster.
In his subsequent chapter, “A Mathematical Meditation on History”, Taleb introduces us to his demiurge, the Monte Carlo generator. The Monte Carlo methods and machine employed by Taleb to recreate on a human scale a summing over histories originated during World War II in the first experiments at Los Alamos designed to simulate the quantum reactions necessary for an atomic explosion. Monte Carlo methods, while relatively crude, and largely dependent on enormous computing power, are also remarkably good at modeling outcomes of complex stochastic processes associated with particle physics (e.g., particle acceleration) and fluid dynamics. Monte Carlo methods also nicely simulate business risk by calculating probability distributions of market behavior.
So Taleb has his own Monte Carlo machine and his own atomic historical units to play with. And with his Monte Carlo generator, he can calculate the chances that his fellow traders will “blow up”, not because their methods are flawed (although surely they are), but because they cannot acknowledge the risks inherent in their trading. These smug traders assume they (and their methods) are infallible. They lack humility. The absence of humility means they may go to Church on Sunday, but they refuse to prostrate themselves before a God whose existence can be inferred (and then only barely) from the multiplicity of historical worlds, the multiplicity of historical identities, the multiplicity of historical realities, the multiplicity of historical outcomes, including for traders.
It bears repeating, the truth that both Donnie and Taleb present us: we think we live in the only possible reality, and that presumption justifies the arrogance of the successful and crushes the souls of the failures. The role of the Jeremiah is to deliver justice by driving home the idea that all of us live by the grace of God, and God may be nothing more than a giant Monte Carlo generator.
Taleb and Frank the Bunny
Taleb echoes Frank the Bunny in the sense that both are Jeremiadic tricksters. One does not hear echoes of Puritan sermonizing. Instead, one witnesses exercises in ridicule and destruction. The onslaught of water and fire in Donnie Darko destroys only that which already destroys – a school that uses religion and dogma to punish and bind its students, and a pedophilic charlatan. By the same token, Taleb uses playful language to skin away the fakery and false claims of Wall Street charlatans. Both Frank the Bunny and Taleb valorize humility and a kind of grace that arises from the awareness of fragility in this world. Perhaps it is from this fragility, this thinness of the border and boundaries of our reality and our identity, that we can best adduce the existence of histories that simultaneously track paths through our minds.