Articles

“Complex systems—the term of art for many interacting agents, whether buyers and sellers in markets, employees and managers in companies, or the atoms and molecules of a turbulent river—have earned that term for a reason. Their most interesting questions rarely have simple answers.” Safi Bahcall, Loonshots (2019) Complex systems are collections of simpler components that […]

“In the absence of feedback loops, the natural distribution of phenomena would be 50/50—inputs of a given frequency would lead to commensurate results. It is only because of positive and negative feedback loops that causes do not have equal results.” Richard Koch, consultant and investor famous for the 80/20 rule Complex systems are collections of […]

In complex systems (such as the human body, companies, or nature), collective behaviors can create dynamics that cannot be defined or explained by studying the parts on their own. These “emergent” behaviors are result from the interactions between the lower-level components of a system and the relationships (or feedback loops) between them. For example, in […]

Leverage points are places within a complex system—such as a corporation, an economy, a city, or an ecosystem—in which a small shift in input force can produce amplified changes in output force.1 When concentrated towards the most critical areas for improvements, even small shifts in our efforts can cause large, durable changes. If we care […]

Dynamic equilibrium describes the balancing cycle that occurs between two phases coexisting on the edge of a phase transition (in so-called “phase separation”), such that neither phase overwhelms the other. Dynamic equilibrium is the goal-state of balancing (negative) feedback loops, which counteract change in an effort to maintain stability. Consider how a thermostat maintains the […]

Complex systems—such as organizations, governments, ecosystems, planets, or galaxies—tend to exhibit different properties and, consequently, to behave differently depending on their current relative size. Put simply, things that happen at a smaller scale may happen very differently—or not all—at a larger scale. If scale didn’t matter, then all relationships would be linear. More of one […]

“I may be wrong and you may be right, and by an effort, we may get nearer to the truth.” Karl Popper, The Myth of the Framework (1994) Scientific theories are explanations—statements about what is there, what it does, and how and why. The distinctive creativity of human beings manifests in our capacity to create […]

Everything we know about the world is a model, a simplified representation of something. This includes every word, language, map, math equation, statistic, document, book, database, and computer program, and our “mental models.”1 We use models constantly to simplify the world around us, to create knowledge, and to communicate. Our mental models, the collection of […]

For much of human history, we relied on authority figures to tell us what is true and just, based on the presumed wisdom of the leaders of our tribe, government, church, etc. The break from this authoritarian and anti-progressive tradition began with the boldness of ancient philosophers such as Aristotle, but truly accelerated in the […]

A counterfactual is a “what-if” scenario in which we consider what could have been or what could happen, rather than just what actually happens. What if I had never met my partner? What if the US had never invaded Iraq? How might our customers react to a price increase? Thinking in counterfactuals is an essential […]

“In reality, a substantial proportion of all evolution on our planet to date has occurred in human brains. And it has barely begun. The whole of biological evolution was but a preface to the main history of evolution, the evolution of memes.” David Deutsch, The Beginning of Infinity (2011, pg. 380) Memes are ideas that are replicators, the broader term for any entities capable of causing themselves to be copied. These aren’t limited to funny internet posts. Memes could include jokes, languages, cultural traditions, artistic movements, business strategies, advertising jingles, scientific theories, conspiracy theories, religions, documents, or recipes. Each of […]

“(T)here is no fundamental barrier, no law of nature or supernatural decree, preventing progress. Whenever we try to improve things and fail, it is… always because we did not know enough, in time.” David Deutsch, The Beginning of Infinity (2011, pg. 212) In today’s news and social media environment, optimism is scarce. We are constantly bombarded with claims that society is heading in the wrong direction, that our children will be worse off, that some problem or trend will ensure our demise. These pessimistic messages poison the conversation around a variety of threats: climate change, artificial intelligence (AI), nuclear apocalypse, […]

Exponential growth occurs whenever a stock of some material or quantity is able to increase or replicate itself in constant proportion to how much there already is. This is a multiplicative effect, in which each step is more extreme than the preceding one. As an example, consider a stock of 1,000 hogs that, given its […]

A power law describes the relationship between two variables in which one variable varies as an exponent of the other. For example, if the side of a square is doubled, the area is multiplied by a factor of four. Power laws are nonlinear relationships, where the collective output changes by more than the proportional change […]

Linear thinking comes naturally to us because our intuition about reality is formed through our (limited) direct experiences, which frequently resemble linear relationships (straight lines on a graph). This thinking serves us well in most parochial circumstances, but it can also lead us astray. We are using linear reasoning every time we say that if […]

“Spend each day trying to be a little wiser than you were when you woke up. Discharge your duties faithfully and well. Step by step you get ahead, but not necessarily in fast spurts… Slug it out one inch at a time, day by day. At the end of the day—if you live long enough—most […]

A local optimum is a solution that is optimal within a neighboring set of candidate solutions—a point from which no small change can generate improvement. However, this local peak may still be far from the global optimum—the optimal solution among all possible solutions, not just among nearby alternatives. This valuable model can teach us about […]

The basis of geometry is symmetry, which describes the property of an object being unaffected by administering some transformation or taking an alternate perspective. Consider an equilateral triangle. If we move the whole shape an inch to the right, the angles and dimensions of the triangle are unchanged; they are symmetrical with regards to that […]

“Here, on the edge of what we know, in contact with the ocean of the unknown, shines the mystery and beauty of the world. And it’s breathtaking.” Carlo Rovelli, physicist Despite our human programming to detect patterns and seek causes or explanations for everything we observe, many events in the world are simply chaotic and […]

“The theory of probability is a system for making better guesses.” Richard Feynman, The Feynman Lectures on Physics (1963, Vol I pg. 6-1) Very few important decisions provide us with the luxury of certainty. Indeed, life involves an endless stream of guesses about the future, from deciding whether to carry an umbrella today to whether […]

Bayesian reasoning is a structured approach to incorporating probabilistic thinking into our decision making. It requires two key steps: Obtain informed preexisting beliefs (“priors”) about the likelihood of some phenomena, such as a suspect’s DNA matching the evidence, a candidate winning an election, or a company achieving its revenue forecast. Update our probability estimates mathematically […]

The Law of Large Numbers is a theorem from probability theory which states that in normally distributed systems, as we observe more instances of a random event, the actual outcomes will converge on the expected outcomes. In other words, when our sample sizes grow sufficiently large, the results will settle down to fixed averages. The […]

The probability distribution of a random variable defined by a standard bell-shaped curve is known as the normal distribution, which has a meaningful central average (or “mean”) and increasingly rare deviations from the mean. It is a symmetrical distribution in which we expect any random observation to be equally like to fall below or above […]

Regression to the mean is the statistical rule that in any complex process that involves some amount of randomness, extreme observations will tend to be followed by more “mediocre” observations. Although regression to the mean is not a natural law but a statistical tendency, it is an extremely useful mental model, because we have a […]

The expected value of a process subject to randomness is the average of its outcomes, each weighted by its probability. We might use expected value to evaluate a variety of phenomena, such as the flip of a coin, the price of a stock, the payoff of a lottery ticket, the value of a bet in […]

A fundamental objective of exploring data is to unearth the factors that explain something. For example, does a new drug explain an improvement in a patient’s condition? Does the DNA evidence match the suspect’s? Does the new product feature improve user engagement? The reigning theory of knowledge, Karl Popper’s critical rationalism, tells us how we […]

Albert Einstein’s groundbreaking theories of relativity demonstrated that time and distance are relative notions, and that they are really two parts of the same thing—a fourth dimension we refer to as “spacetime.” A point in spacetime, called an “event,” is both a location and a moment. According to Einstein’s “special theory of relativity” (1905), relationships […]

If an object is left alone, if no other force (such as friction) acts upon it, it will resist changes in its state of motion. Objects already in motion will continue to move forward with a constant velocity, and stationary objects will continue to stand still—unless another force intervenes.1 The more massive the object, the […]

A phase transition is the process of change between different states of a system or substance, which occurs when one or more of the system’s control parameters crosses a “critical” threshold. We tend to take stability for granted, leading us to be caught off-guard when the ground shifts between our feet. By better understanding the […]

“The ultimate purpose of life, mind, and human striving: to deploy energy and information to fight back the tide of entropy and carve out refuges of beneficial order.” Steven Pinker, The Second Law of Thermodynamics (2017) In the realm of thermodynamics, the term “entropy” represents the measure of disorder or randomness in a system. While […]

Until around the 19th century, we generally assumed that some supernatural force (such as the Greek gods) was required to explain the unique behavior of matter in living organisms. Then, Charles Darwin’s theory of evolution in 1859 explained the origin of life in terms that required no special physics. Its modern formulation involves three main […]

Every time that we attempt to transmit information (a “signal”), there is the potential for error (or “noise”), regardless of whether our communication medium is audio, text, photo, video, or raw data. Every layer of transmission or interpretation (for instance, by a power line, radio tower, smartphone, document, or human) introduces some risk of misinterpretation. […]