How to Expect the Unexpected

1. Gut Feelings Are Often Unreliable

Trying to foretell the future helps us to feel in control of its inherent uncertainties, to manage our aspirations and to make important decisions.

Instinct vs. Evidence. Humans have a natural desire to predict the future, often relying on intuition or "gut feelings." However, these methods, lacking scientific basis, are generally unreliable. Throughout history, bizarre and unscientific methods have been used for fortune-telling, none proving more reliable than others.

Ancient divination methods. Ancient cultures employed various forms of divination, such as cleromancy (casting lots), tasseography (interpreting tea leaves), and haruspicy (examining animal entrails). These practices sought to interpret the will of gods or divine truth through random patterns or events. For example:

• The I Ching used yarrow stalks or coins to generate hexagrams for interpretation.
• The Yoruba practiced Ifá divination by casting kola nuts to create binary patterns.
• Haruspicy involved examining animal entrails for omens.

Randomness and interpretation. Randomness plays a key role in these practices, with diviners interpreting unpredictable signs to provide personalized messages. However, the illusion of randomness can be exploited to manipulate outcomes and convince individuals of the diviner's abilities.

2. Expect the Everyday Extraordinary

When coincidences appear without warning they can send us sprawling in search of the reasons behind them.

The illusion of improbability. Seemingly impossible coincidences occur more often than we realize. Our egocentric perspective makes it difficult to grasp the likelihood of such events at a population scale.

Examples of coincidences:

• Discovering a train ticket with "P AUST" in a Paul Auster book.
• Winning the lottery or experiencing a series of unlikely events.
• Spotting a pattern in the numbers in the lottery or on the roulette wheel.

The law of truly large numbers. Given enough opportunities, even highly improbable events are bound to happen. This principle explains why coincidences, though seemingly rare, are actually quite common when considering the vast number of possibilities.

3. Mastering Uncertainty Requires Objectivity

Mathematics can provide us with the objective tools to bypass the foibles of our own biology – the limitations imposed by our own thought processes, the compulsions that ultimately make us human, but let us down when it comes to making inferences about the world around us.

Human biases in randomness. Humans are not naturally equipped to reason in the face of randomness and uncertainty. Our brains tend to seek patterns and meaning, even in noisy environments, leading to overgeneralizations and incorrect conclusions.

The Texas sharp-shooter fallacy. This fallacy involves drawing a conclusion based only on data that supports a hypothesis, while ignoring data that contradicts it. This can lead to the mistaken identification of clusters or patterns in random distributions.

Multiple comparisons fallacy. Performing numerous statistical tests on a single dataset increases the likelihood of finding a seemingly significant result by chance. To avoid this, scientists should limit the number of questions they ask and correct for multiple comparisons.

4. Changing Your Mind Is a Strength, Not a Weakness

Scientific theories are nothing more than epistemic predictions about the nature of reality that haven’t been proved wrong.

The importance of adaptability. Being able to update one's beliefs in light of new evidence is a hallmark of rational thinking and scientific progress. Rigid adherence to prior convictions, even in the face of contradictory information, can lead to errors and missed opportunities.

Bayes' theorem. This theorem provides a framework for updating beliefs based on new evidence. It combines prior probabilities (initial beliefs) with the likelihood of observing new data to arrive at posterior probabilities (updated beliefs).

Key lessons from Bayes' theorem:

• New evidence isn't everything: Prior beliefs matter.
• Consider different viewpoints: Explore alternative hypotheses.
• Change your opinion incrementally: Update beliefs gradually as new information accrues.

5. Strategic Thinking Requires Understanding the Game

As well as suggesting ways in which we can try to predict the future, perhaps more fundamentally, this book is about identifying and understanding the barriers we come up against when trying to do so.

Game theory basics. Game theory provides a framework for analyzing strategic interactions between rational actors. It assumes that individuals act in their own self-interest to maximize their expected payoffs.

The prisoner's dilemma. This classic game illustrates how individual rationality can lead to suboptimal outcomes for the group. Mutual cooperation is often the best strategy, but the temptation to defect can lead to mutual defection.

First-strike advantage. In some games, striking first can provide a significant advantage, making conflict more likely. However, the costs of long-term conflict often outweigh any initial gains.

6. Linearity Bias Distorts Our Perception of Reality

One of the most important cognitive economisations, whose ubiquity I expose in Chapter 6, is linearity bias – the propensity to believe that things will stay constant or continue to change at a consistent rate.

The allure of straight lines. Humans have a natural tendency to assume that relationships between variables are linear. This can lead to inaccurate predictions and poor decision-making in situations where nonlinearity is present.

Examples of nonlinear relationships:

• The reciprocal relationship between fuel consumption and fuel efficiency.
• The exponential growth of infected people at the start of an epidemic.
• The quadratic relationship between the diameter of a pizza and its area.

The importance of recognizing nonlinearity. Being aware of nonlinear relationships can help us avoid common pitfalls and make more informed choices in various aspects of life, from environmental decisions to financial investments.

7. Positive Feedback Loops Can Quickly Escalate

Nonlinearity, which we will discover in the later chapters of this book, is the second confounding factor (alongside probability) that foils our naïve attempts at prediction.

Amplifying effects. Positive feedback loops occur when a signal triggers a response that amplifies the original signal, creating a self-reinforcing cycle. This can lead to rapid and unexpected escalation.

Examples of positive feedback loops:

• The exponential growth of infected people during an epidemic.
• The ice-albedo feedback loop, where melting ice exposes darker surfaces that absorb more heat.
• Stock market bubbles, where rising prices attract more investors, further driving up prices.

The snowball effect. Positive feedback loops can start small but quickly gather momentum, leading to dramatic and often uncontrollable outcomes. Understanding these loops is crucial for managing complex systems.

8. Negative Feedback Loops Can Cause Unintended Consequences

We assume that things will continue linearly – just the way they are now. It causes us to minimise, question or disregard warnings of imminent threats, because they are so far beyond the realm of our experience as to make them unbelievable.

Stabilizing forces. Negative feedback loops act to dampen or reverse changes, maintaining stability in a system. However, these loops can sometimes lead to unintended consequences.

Examples of negative feedback loops:

• The body's thermoregulation system, which maintains a stable temperature.
• The use of pre-match rituals by sportspeople.
• The von Restorff effect.

The Streisand effect. Attempts to suppress information can backfire, drawing more attention to it. This is an example of a negative feedback loop where the attempt to reduce visibility actually increases it.

9. Chaos Limits Long-Term Predictability

Although mathematics gives us an unprecedented tool with which to project forwards, uncertainty and nonlinearity place definitive horizons on how far we can ever hope to see into the future.

The limits of prediction. Even with sophisticated mathematical models, there are fundamental limits to how far we can predict into the future. Chaos, characterized by sensitive dependence on initial conditions, can make long-term forecasts impossible.

The butterfly effect. This concept illustrates how small changes in initial conditions can lead to drastically different outcomes in chaotic systems. It highlights the inherent unpredictability of complex phenomena like the weather.

The importance of understanding chaos. Recognizing the limits of predictability can help us avoid overconfidence in our forecasts and make more informed decisions in the face of uncertainty.

Last updated: February 22, 2025