The Value of Stochastic Thinking

Leo Tolstoy’s War and Peace is, of course, as much a meditation upon history and human agency as it is a novel that explores the lives of several interconnected aristocratic Russian families against the backdrop of the Napoleonic wars.

Among the many philosophical themes that Tolstoy’s epic novel explores are the tension between individual agency and larger economic, historical, political and sociological forces; the nature of historical causation; the role of chance and randomness in human life; women and men’s quest for meaning and purpose in love, family, religion and wartime sacrifice; the nature of power and authority within a highly hierarchical polity; and the personal transformation and moral growth prompted by the experience of war, loss and suffering.

If any single theme can be said to run through such a sprawling work of literature, it is contingency—that historical events and individual lives are shaped by a combination of individual actions and unpredictable events and circumstances, rather than determined by impersonal forces or laws. Highly critical of determinism, the doctrine that human actions and events are caused solely by forces external to people’s individual will, Tolstoy demonstrates that the course of events is influenced by chance, individual agency and a wide range of social and cultural factors.

A rejection of the great man theory of history, the claim that historical events are governed by the actions and decisions of world historical figures, history’s heroes, leaders or villains, War and Peace suggests that historical outcomes are the product of a complex interplay among circumstances, social structure, cultural norms, accident and the collective actions and choices of diverse individuals.

Also, the novel is a reflection upon history’s meaning, as Tolstoy’s characters struggle to make sense of the past, its impact on the present and any lessons that it might offer the future.

I mention War and Peace because Tolstoy’s emphasis on contingency and unpredictability can be found in many recent currents of thought in the humanities and the social and natural sciences. This development is manifest in the increasing frequency of usage of the word “stochastic” not just in scholarship but in the popular press.

The word “stochastic” appeared in 12 New York Times articles in the past year. An adjective used to describe processes, events or systems that involve chance, randomness, uncertainty and probability, the term was used in articles that examined:

• Stochastic terrorism—the seemingly random acts of violence that “are, in fact, provoked by ‘coded language, dog whistles and other subtext’ in statements by public figures.”
• Dynamic stochastic general equilibrium models—the impact of macroeconomic policy changes on different sectors of the economy.
• The electronic music pioneer Iannis Xenakis’s concept of stochastic music—an approach to music composition in which sound is constructed not out of “notes, but by ever-changing glissandos going up and down and landing briefly into visceral clusters of pitches.”
• Stochastic AI modeling—in which machine learning algorithms rely on predictive analytics in order to predict people’s behavior or political views or sexual orientation.
• Stochastic societal turbulence—how corruption, violence, trolling and sexual scandal are portrayed in recent streaming dramas and comedies and their impact on individual lives.
• Stochastic resonance—a popular theory that claims that “the presence of white noise allows the brain to tune into hard-to-hear tones—in music, people’s voices or ambient sounds—that otherwise go unnoticed.”
• Stochastic quantum mechanics—the hotly debated interpretation of quantum mechanics that introduces probabilistic and random elements into the description of quantum systems.

In a stochastic process, outcomes are not entirely predictable or deterministic, but rather subject to random variations or uncertainties.

Let’s look very briefly about how the concept has been applied across the academy.

In economics, stochastic concepts and models are increasingly used to model the unpredictable and uncertain impact of natural disasters, technological innovation, fluctuations in consumer behavior, supply chain disruptions and shifts in monetary and fiscal on economic growth; to forecast market behavior in response to shifts in interest and exchange rates and asset prices; and to optimize economic decision-making.

In history, stochastic concepts have offered a way for historians to navigate between the Scylla of individual and collective agency and the Charybdis of determinism and impersonal historical forces. Although the term “stochastic” is not invoked as often as in other disciplines, the ideas that underlie the concept—causal complexity, unpredictable or ironic outcomes, and the influence of unforeseeable factors—are widely embraced.

A stochastic approach encourages historians to conceive of historical change in in nonlinear terms and to consider counterfactual scenarios and rigorous comparison. Key stochastically informed historical concepts include:

• Contingency—the role of accident, chance and individual decisions on the course of history.
• Conjunctures—those moments of crisis when a combination of events and circumstances create opportunities for critical, weighty decisions to take place; and
• Context—the social, political, intellectual, cultural and economic conditions that existed during a certain time and place and that shape available options. Also, important aspects of context are “historical forces”—the broad demographic, economic, environmental, ideological, political, religious, social and technological processes that help drive historical change and shape societal developments, decisions and events.

In philosophy, stochastic thinking, with its emphasis on chance, uncertainty, indeterminacy, probability and randomness, is reshaping the subfields of epistemology, metaphysics and ethics, as well as theories involving causality, determinism and free will, modeling, moral responsibility, risk and the nature of time.

For example, in Bayesian epistemology, beliefs are subjected to probability theory and are evaluated based on accumulated evidence. In metaphysics, a stochastic-informed approach examines how indeterminacy and chance influence the human ability to understand reality; explores the role of chance and randomness in the emergence of complex phenomena; and treats causation as a matter of probability rather than of strict determinism. A stochastic approach to ethics, in turn, considers the probabilistic outcomes or consequences of moral actions.

In psychology, stochastic processes are used to understand learning, which is influenced by fluctuations in attention, motivation and cognitive resources, and neural and cognitive processing and decision-making, including variations in memory retrieval and cognitive response time and accuracy and the influence of random fluctuations in synaptic transmission and cellular and hormonal functioning.

In the physical sciences, the stochastic emphasis on randomness and probability has left a mark on statistical and quantum mechanics, thermodynamics, the behavior of polymers, the dynamics of chemical reactions and the functioning of electronic circuits, neural networks and climate systems.

In sociology, stochastic models help sociologists understand the formation, dynamics, persistence, impact and dissolution of social networks and social movements, and population dynamics, including the impact of fertility decisions, immigration, civil conflict and war and economic volatility.

How to think about causation within complex systems, in which chance events and multiple variables are at play, is among the great challenges of our time. This is a subject not only of interest to economists, historians, philosophers, psychologists, physical scientists and sociologists, but to anyone interested in stock market behavior, weather prediction or the likelihood of international tensions descending into armed conflict.

A stochastic approach recognizes that outcomes are, in part, by-products of chance and randomness and that causation is probabilistic rather than inevitable or predetermined. It requires us to evaluate all the factors that can contribute to an outcome, whether these are cognitive, environmental, genetic and social in the case of psychology; agency, context, interacting causes and structure, in the case of history; and social structure, institutional dynamics, culture, social class, gender, race and ethnicity, in the case of sociology—and recognize that random variations will result in unpredictable results.

By rejecting strict determinism, a stochastic perspective reminds us that outcomes, whether in sports, politics or everyday life, hinge on complex contingencies that we mustn’t ignore. It’s this contingency that should remind us not only of the vital importance of chance, accident, coincidences and decisions in life, but of our agency, our subjectivity and our ability to make choices and decisions, exercise our capacity to act and take responsibility for our actions.

In very different ways, scholars across the disciplinary spectrum are grappling with themes that lie at the very heart of Tolstoy’s War and Peace and Fyodor Dostoyevsky’s The Brothers Karamazov and that anticipate ideas central to existentialist thought. It’s our job to find design and meaning in a seemingly random and unpredictable universe; uncover the processes that drive, but don’t determine, outcomes and behavior; and face up to the ethical challenges of living in a world that lacks objective moral values.