On June 15, 1919, Karl Popper left his family’s Vienna apartment to join several thousand demonstrators marching to demand that the government free a group of jailed communists. Half the protestors were communists, others teenage boys. The sixteen-year-old Karl Popper was both. Just before noon, the crowd broke into a run and approached Vienna’s Hörlgasse shouting for guards to release the prisoners. In that narrow street, the protesters collided with a cordon of police on foot and horseback, breaking the wave and leaving them facing off with the police.¹ The police would later be criticized for their brutality, but they had every reason to fear the worst. The previous evening they had arrested more than a hundred communist leaders based on a reliable tip that they planned to incite demobilized troops to a putsch the next day. A month earlier, a demonstration by thousands of unemployed workers and ex-soldiers in front of the Parliament had turned violent, costing several policemen their lives.

Vienna had been in turmoil for much of the past year. As World War I drew to a close the preceding year, the Austro-Hungarian military disintegrated, losing a series of key battles and suffering widespread mutiny among the troops. The Allied forces, to end the war more quickly, quarantined Vienna to starve the Austrians into submission, causing food riots and near famine.² After the war, the victorious Allies carved the former Hapsburg Empire into independent states including Hungary, Czechoslovakia, Poland, and the State of Slovenes, Croats, and Serbs. “Austria,” the French prime minister Georges Clemenceau observed acidly, “is what is left,” with a population one-sixth its former size. The country suffered from widespread unemployment and hyperinflation. The currency lost half its value in the first six months of 1919 and would go on to lose 90 percent by the end of the year, decimating a lifetime of savings for many Austrian citizens.³ Joseph Schumpeter, who later coined the phrase “creative destruction,” was the minister of finance until he was sacked in November of that year.

As the protestors grew agitated in the Hörlgasse, the police commander warned them to refrain from violence. According to eyewitness accounts, a teenage boy wearing a brown suit and hat approached a mounted policeman and tried to unseat him. When the officer resisted, the boy pulled a pistol hidden inside his jacket and fired one shot at close range, hitting the policeman in the stomach. Several other protestors produced handguns and shot at the police. The officers maintained their discipline, firing three warning shots into the air, but when the mob failed to disperse, they opened fire. Most of the crowd—including Popper—was unarmed and unaware of the planned putsch. Popper fled during the exchange of gunfire, but not before witnessing fellow protesters fall yards from where he stood.

MENTAL MAPS

In plotting their putsch, Vienna’s communists followed a path laid out decades earlier by Karl Marx and elaborated by later thinkers. A political theory, such as Marxism, is an example of what I call a mental map, a model that represents reality and serves as a guide to action. Maps are not limited to politics: scientists formulate theories to focus their data collection and experimentation; generals develop strategies to deploy troops; coaches draw up game plans to neutralize opponents’ best players; entrepreneurs write business plans to secure funding and focus their limited resources. Some mental maps are explicit, others largely implicit, but all perform three specific functions: they emphasize important categories, clarify relationships among variables, and suggest appropriate action.

Mental maps draw selected variables to the fore while nudging less important factors into the background or leaving them off the map altogether. Socialist theory emphasized different classes—for instance, capitalists, workers, and the lumpenproletariat (whom Marx defined as the “flotsam of society”). Categorizing people by economic class rather than, say, religious affiliation or nationality, highlighted the gap between wealthy owners and struggling laborers.

The choice of categories depends on what the user hopes to accomplish. A driver will choose a city map showing streets and highways, while a politician might represent the same terrain with a house-by-house analysis of political party affiliation and past campaign donations. Managers looking to increase their firm’s profits might adopt Professor Michal Porter’s model of competitive strategy, which specifies five forces that influence the profitability of companies within an industry.⁴

The most useful mental maps not only highlight important variables but also spell out interactions among them. In socialist theory, class struggle described the ongoing battle between different classes to control the means of production, such as factories and mines. Conflict rather than cooperation drove progress, according to this map, and could only end in complete victory for one class. Porter’s Five Forces model assumes a similar zero-sum competition for profits, where suppliers, competitors, and customers struggle for a larger slice of a finite profit pie.

By charting the terrain, mental maps suggest effective action. The socialist theory of class struggle ruled out compromise and exhorted activists to bring latent class conflict to a head through violence. Hence Vienna’s communists plotted a putsch rather than running for elected office. The Five Forces model suggests that managers first choose a profitable industry to enter and then erect barriers to entry to keep rivals, suppliers, and customers from capturing a disproportionate share of profits.

QUESTION MARX

When Popper joined the communist party in the spring of 1919, he failed to conduct intellectual due diligence on the mental map that guided the party. At that time, a host of contending movements, including anarchism, fascism, and pacifism, offered competing explanations of the turbulence that plagued Europe in the opening decades of the twentieth century. By 1919 socialism had emerged as an article of faith among Vienna’s intelligentsia, and Popper accepted it without critical analysis.

After the demonstration, Popper scrutinized the theory that left corpses in the street. How, he wondered, could the communists be so sure their comrades’ sacrifice was justified? How did they know that the fall of capitalism was inevitable or that socialism would be better? In the course of his analysis, Popper discovered that Marxist thinkers saw socialism not as utopian idealism but as hard science. They claimed class struggle was an inevitable law of economics—not a socially constructed law, like a speed limit, but a law of nature akin to gravity. Beneath the fiery rhetoric of the revolution lay the cool certainty of science.

When Popper looked under the hood of Marxist theory, he was appalled to find neither science nor truth but a creed riddled with obvious “gaps and loopholes and inconsistencies.”⁵ Not only did the doctrine suffer from deep theoretical flaws, but the most critical predictions failed real-world tests. Marx predicted that manufacturing-intensive countries, such as England and Germany, would produce the class conflict required to usher in socialism. These countries failed to follow Marx’s script, however, and the only revolution of the time took place in agrarian Russia, one of the least industrialized economies in Europe. Despite theoretical flaws and faulty predictions, millions of people clung to Marxism. Angry with himself for embracing a flawed doctrine, Popper rejected it.

In 1919, events conspired to undermine not only political certainties but also most of the established truths that might, in a more stable era, have shaped Popper’s future. The dissolution of the Hapsburg Empire demolished bourgeois confidence in the link between hard work and middle-class security. Popper’s father, Simon, was born in modest circumstances in a small Czech town and later migrated to Vienna, where he rose to prominence in legal circles. Contrary to the modern stereotype of the workaholic lawyer, Popper’s father relaxed by writing poetry and translating Greek and Roman literature into German.⁶ When Simon Popper turned sixty-three in 1919, he looked forward to a retirement spent in his personal library. Instead, the collapse of the Austrian currency decimated a lifetime of savings and forced the elder Popper to continue working. Karl Popper moved to low-cost student housing to ease his family’s financial burden.

As if it weren’t enough that the apparent certainties of Marxism, empire, and middle-class security were upended, that same year saw the laws of physics overturned as well. In November 1919, the Times of London, a paper not prone to hyperbole, ran the headline “Revolution in Science, New Theory of the Universe, Newtonian Ideas Overthrown.”⁷ For two centuries Isaac Newton’s laws of motion and universal gravitation had been accepted as a true representation of nature. In 1905, Albert Einstein, a patent clerk working in Bern, Switzerland, proposed a new view of the universe in which gravity could distort space. Based on his theory, he predicted that light passing by a massive object should curve slightly toward it rather than follow a straight path, as Newtonian physics predicted. On May 29, 1919, the English astrophysicist Arthur Stanley Eddington conducted an elegant experiment that proved light did indeed bend when it passed the sun.

PROVISIONAL KNOWLEDGE

Taken together, the events of 1919 seared a single insight upon Karl Popper: that all maps leading into the future—be they political agendas, personal plans, or predictions based on scientific theories—are provisional. They remain subject to rejection in light of disconfirming evidence. His experiences, Popper later wrote, “taught me the wisdom of the Socratic saying, ‘I know that I do not know’…and impressed on me the value of intellectual modesty.”⁸

Any map that makes predictions about the future, according to Popper, whether derived from scientific theories such as Newtonian physics or political doctrines such as Marxism, resemble a working hypothesis, which people adopt not because it is true but because it approximates truth closely enough to guide action. These working hypotheses provide imperfect representations of a complex and fluid world. Popper compared them to nets woven to catch portions of reality as it swims by, while letting everything else pass through the mesh.⁹ Working hypotheses are always flawed because they reduce complexity to simplicity, omit critical variables, and remain stable as the world turns.

If you scent a whiff of intellectual paranoia here, trust your nose. Popper’s views on provisional knowledge imply that all our maps eventually let us down. Millions of passionate believers in Marxism did not make the creed true, just popular. Widespread consensus did not mean that Iraq possessed weapons of mass destruction, nor does it prove that the earth’s temperature will continue to rise in the future. Our theories about the future, without exception, remain subject to revision or rejection in light of new knowledge that might arise in the future. All our theories will let us down; we just don’t yet know how or when.

In the early twentieth century, most scientists viewed hypotheses as theories that had not yet been proven. Popper turned this view on its head and argued that any theory—even one as well established as Newtonian physics—was simply a hypothesis that had not yet been disproved. For Popper, science was a Darwinian struggle, where competing theories, all flawed in some way, struggled to survive rigorous testing in the real world. Scientists frame a hypothesis, submit it to severe investigation, and abandon their theory if it fails the test. Rigorous testing weeds out the weaker theories, leaving only the strong to survive, until further experiments expose their flaws and they too are replaced by even stronger theories. Science, for Popper, was permanent revolution.

THE CYCLE OF CONJECTURE AND REFUTATION

The engine that drives scientific revolution, in Popper’s view, was a cycle that iterated between conjecture and refutation.¹⁰ The cycle begins when a scientist bypasses a theory’s explanatory strengths to search out its weak spots. Prior to formulating the special theory of relativity, Einstein studied both mechanics and electrodynamics with an eye to identifying their limitations. These shortcomings typically manifest themselves as anomalies, unusual findings that fall outside existing categories or defy explanation by established theory. An anomaly points in the direction of a mismatch between a simplified theory and complex reality, and flags a productive spot for further exploration.

In the next step, the investigator formulates a working hypothesis to explain the anomaly. This stage demands the intellectual courage to break cleanly with conventional wisdom and the imagination to envision a creative alternative. Popper idolized Einstein for having the audacity to conceive of an alternative view of the universe while working as a patent clerk. Popper separated problem identification from hypothesis formulation, but he recognized that they often coevolved in practice, with a hypothesis suggesting a fresh look at the original problem from a different angle.¹¹

Popper termed the third step in the cycle “error elimination.” In this stage, the researcher submits her working hypothesis to severe testing to expose its flaws. Error elimination includes scrupulous analysis of a theory to unearth logical inconsistencies—recall Popper’s critique of Marxism. Error elimination also entails real-world experiments, such as Eddington’s test to determine whether gravity bent light. The best way to eliminate errors, Popper argued, was to design experiments to refute a theory rather than find supporting evidence.

Popper placed particular emphasis on error elimination. He noted an asymmetry between what scientists can prove and what they can disprove. Spotting the millionth white swan, to use one of his best known examples, does not conclusively prove that all swans are white. A single black swan, however, disproves it conclusively.¹² “Human reason is unlimited with regard to criticism,” Popper argued, “yet limited with regard to its powers of prediction.”¹³ Popper spent much of his career critiquing the work of others and earned a reputation as an intellectual giant-killer. Many Marxists considered Popper’s critique the most devastating ever written, while his scathing appraisal discredited the popular philosophical movement known as logical positivism. (Ironically, Popper detested criticism of his own work, forbidding editors to tweak his prose, shunning colleagues who critiqued his work, and browbeating doctoral students in an atmosphere resembling Senate inquiries under Joseph McCarthy.)¹⁴

PROVISIONAL KNOWLEDGE IN THE REAL WORLD

Popper’s insight that all knowledge of the future is provisional belongs to a branch of philosophy known as epistemology, which explores the nature and limits of knowledge—what we know, don’t know, and cannot know. Hard-nosed readers might dismiss these questions as obscure, at best suited to arcane discussions among philosophers of science, at worst relegated to late-night bull sessions in a college dorm room. Popper, however, considered the question of what we can and cannot know profoundly practical. Indeed, one of the best introductions to his thinking is entitled Philosophy and the Real World.¹⁵ Popper spent seven decades teasing out the implications of provisional knowledge for a range of real-world questions: How do scientists know when to reject their theories? Is communism a better way to organize society than capitalism? How can governments avoid imposing disastrous policies?

Few people think of themselves as applied epistemologists. Yet whether they succeed or fail in a turbulent world depends to a large extent on how well they manage the cold reality of provisional knowledge. Take entrepreneurship, for example. Many start-ups begin when an entrepreneur glimpses a potential gap in the market and a way to fill it. Entrepreneurs can jot their map on the proverbial cocktail napkin, create a PowerPoint pitch for investors, or write a business plan replete with market surveys and pro forma projections. These differences in form should not obscure their fundamental similarity—all are mental maps, subject to revision or rejection in light of new information. The definition of the opportunity and the plan to pursue it entail assumptions about the evolution of technology, customer adoption, competitive response, and availability of funding, among others. If these assumptions are wrong, the entrepreneur must rethink the hypothesis or abandon it altogether.

Studies of start-up survival confirm that most entrepreneurs follow flawed maps. Research across a broad range of industries, countries, and time periods finds that more than half of all start-ups go out of business within four years.¹⁶ Just because the others survive does not mean the founders got their map right. Start-ups can limp along for years, barely breaking even, without creating significant value. Those that survive completely revise their map as flaws in the plan become evident. A systematic study of three hundred start-ups found that persisting with the initial business plan was the best single predictor of failure one year after founding—nine of ten entrepreneurs who stuck to their initial business plan without revision failed.¹⁷ To be clear, provisional knowledge is not always bad. Technologies sometimes solve an even bigger problem than the targeted one, markets prove larger or grow faster than expected, and competitors occasionally doze off at the wheel.

Popper’s cycle of conjecture and refutation can help entrepreneurs cope with their provisional knowledge, particularly in a venture’s early years.¹⁸ Aaron Kennedy decided to start Noodles & Company, a chain of restaurants specializing in cooked-to-order noodle dishes from around the world, after he noticed an anomaly. While dining at a pan-Asian noodle restaurant in Greenwich Village, Kennedy was struck that the format was not more common given its healthy fare, speed, and value for money. After spotting a gap in the market, he formulated a conjecture about how to seize the opportunity, and opened one restaurant in Denver and another in Madison, Wisconsin, to test his hypothesis in two different markets.

Noodles & Company’s initial experience was not auspicious. The spring of 1996 brought a scathing review in a Madison newspaper, disappointing financial results for both sites, and flooding in the basement of the Madison restaurant. Kennedy and his team drove from Madison to Chicago to tour successful noodle shops, compare them to their own restaurants, and decide whether to quit or revise their business model. They stuck it out, but only after identifying fifteen changes to their initial plan. They switched from steam tables to sauté lines to increase freshness, for example, and warmed up the restaurants’ color scheme. The Noodles & Company team tested the modified business model in the existing sites and two new ones over the following two years. Once the revised model gained traction, Noodles & Company scaled rapidly.

The venture capital industry has institutionalized the conjecture-refutation loop by staging investments in rounds. Entrepreneurs sometimes bemoan repeated rounds of fund-raising as a distraction from real work. Painful as it may seem in the short term, this iterative approach can help balance execution with revision. Between rounds of fund-raising, an entrepreneur can go into head-down execution mode to test her hypothesis. The need to raise another round of financing forces the entrepreneur and potential investors to reexamine the map and decide whether to plow forward, revise the plan, or cut their losses. This approach works better than questioning the business model every day or pursuing a plan without revision. The box below describes some ways entrepreneurs and managers can design more effective experiments.

WHAT POPPER MISSED

Popper presented a compelling vision of science as endless cycles of conjecture and refutation with fierce competition among theories. Thomas Kuhn, in an influential study of the history of science, describes a reality different from Popper’s idealized vision in every important particular.¹⁹ Instead of competing theories, Kuhn finds that scientists rely on a single paradigm—such as Newtonian dynamics or Einstein’s theory of relativity—to guide their research. The typical scientist is not the lone genius like Einstein, but rather a card-carrying member of a tightly knit community defined by its adherence to a single paradigm. Most scientists resemble devout members of a religious order bound by their vows to a common doctrine. Instead of seeking anomalies, scientists spend most of their time in head-down mode, plugging away at problems that their paradigm deems worthwhile.

When anomalies arise, scientists typically overlook them, ignore them, or patch existing theory with ad hoc tweaks to accommodate the incongruity. Rather than break with the status quo to formulate bold conjectures, scientists spend their days and years practicing “normal science,” extending established knowledge step by incremental step. The history of science, as depicted by Kuhn, consists not of constant revolution but rather of long stretches of normal science within the tight boundaries of the dominant paradigm. Over time, the cumulative pressure of unresolved anomalies grows, and once in a great while it precipitates a crisis where competing theories vie to plug holes in the existing paradigm. After a new paradigm emerges, it grows to dominate the field, and the head-down work of normal science resumes. Revolutions are rare, short-lived, and atypical of how most scientists, in most fields, spend most of their time.

The gap between Popper’s vision and the reality described by Kuhn arises not because practicing scientists fail to achieve a lofty ideal. Rather, Popper’s view is flawed because it overlooks the commitments required for scientific inquiry. A scientific paradigm must represent reality, but it must also induce the long-term commitments required to explore that paradigm. Science cannot progress without major investments of time, attention, and cash. Governments, universities, and scientists themselves seek a stable paradigm before committing these resources.

Consider the funding required to make large-scale investments, such as the €5 billion to construct the Large Hadron Collider in Switzerland. Governmental agencies find it much easier to justify an expenditure based on a stable and widely accepted paradigm. Designing experiments for the collider and interpreting the results involve thousands of scientists and engineers from around the world. A shared commitment to the standard model of particle physics provides them with a common language and framework to decide which experiments are worthwhile and to interpret results.

Scientific progress requires collective action sustained over time, and progress is impossible without stable mental maps. Scientists must invest decades of their lives mastering a body of arcane knowledge, honing highly specialized skills, and building a reputation and network within their fields. Few make such commitments unless they believed the paradigm will persist long enough for them to earn a return on their investment. Persevering within a paradigm sometimes allows scientists to resolve stubborn anomalies. The moon’s actual perigee (the point in its orbit when it is nearest to earth) was twice that predicted by Newton’s theory, a glaring anomaly that stumped scientists. Rather than abandon the model, however, scientists continued to work within the Newtonian paradigm for decades. Their persistence paid off when a French mathematician worked out that past applications of the theory, rather than the theory itself, accounted for the discrepancy, and resolved the anomaly.

Popper saw scientific theories as nets to capture reality, but Kuhn recognized that they play another role as well. Mental maps attract the funds, effort, and attention required to explore the map. Every mental map, from a start-up business plan to a presidential policy agenda, is both a flawed representation of reality and a tool to secure long-term commitments. These two roles work at cross-purposes. To represent a turbulent world, the ideal map is complex enough to encompass a multifaceted reality, fluid enough to adapt as circumstances change, and loosely held enough to be discarded when proven wrong. To secure commitments, however, a map should be simple enough to communicate widely, sufficiently stable to induce long-term commitment, and firmly held enough to inspire confidence. The two roles tug a map in different directions—turbulence calls for constant change, while commitment demands stability.

“The test of a first-rate intelligence,” F. Scott Fitzgerald noted, “is the ability to hold two opposed ideas in the mind at the same time and still retain the ability to function.”²⁰ The conflicting roles played by mental maps produce what I call the map paradox: in a turbulent world, people must make long-term commitments based on a mental map they know to be flawed. The paradox arises in any situation where progress requires both long-term commitments from many people and adaptation to changing circumstances. In other words, the map paradox arises when grappling with most important issues, including health care reform in the United States, repairing the global financial system, reversing climate change, and negotiating peace in war-torn regions, as well as the personal concerns of running a company or raising a family. There are exceptions, of course—mutual-fund managers face turbulence but can easily reverse their positions. By and large, however, anything worth doing in a turbulent world requires people to act as if their map is right, know it is wrong, and retain the ability to function.

The map paradox is not a new problem. It has dogged philosophers for millennia. Consider the Skeptics, a school of philosophy in ancient Greece who first articulated the problem of provisional knowledge. The Skeptics distrusted all knowledge and feared seduction by accepted beliefs. Skeptics honed techniques to resist uncritical belief. They raised objections to arguments others accepted blindly. The Greek word aporia, often translated as “roadblock” or “impasse,” described the objections Skeptics threw in the path of any speaker making an argument. Skeptics reminded interlocutors that “for every argument there is an opposing argument of equal weight.”²¹ The Skeptic philosopher Sextus Empiricus, for example, would set out the arguments in favor of and against any proposition with equal rigor, regardless of which side he believed. The practice of eliciting arguments on both sides helped check the tendency to accept arguments because they were popular, comforting, or supported by a powerful advocate.

Over the centuries, many rulers, soldiers, and administrators adopted a skeptical stance toward knowledge but faced a practical challenge—how to act decisively in the face of provisional knowledge. Tallying up both sides of an argument often results in a draw, indecision, and inaction. A constant onslaught of objections can bring an argument to a grinding halt. Rigorous skepticism, while intellectually honest, hinders action. To avoid this dilemma, some ancients relegated their skepticism to metaphysical matters, refusing to commit to a view of God, for instance. Faced with the demands of daily life, where they had to commit time, attention, or money, they conformed to established custom and tradition.

Blindly following the crowd in practical affairs, however, eliminates whatever benefits skepticism might bring in practice. The Scottish philosopher David Hume believed dogmatism, an unshakable belief in a doctrine, was unavoidable. To him, people were incapable of reconciling the provisional nature of knowledge with the practical demands of everyday life. If people took seriously the incomplete nature of what they believed, Hume argued, “all discourse, all action would immediately cease, and men remain in a total lethargy, till the necessities of nature, unsatisfied, put an end to their miserable existence.”²² People could not afford to recognize the provisional nature of knowledge, Hume argued, and instead must pretend that their maps were truth. Absent this fiction, they could not function.

Is the map paradox, in the end, unmanageable? Are we destined to choose between skeptical indecision and dogmatic action? Must we continue to lay down horrendous sacrifices at the altar of false theories, like Vienna’s communists? Can the extraordinary genius alone manage this tension, leaving the rest of us a choice between two deeply flawed alternatives?

The map paradox cannot be eliminated, but it can be successfully managed. Indeed, seizing the upside of turbulence demands it. It is easy to simplify the paradox by ignoring either the reality of provisional knowledge or the necessity of commitment. Scarred by his experience with socialism, Popper considered commitment to any point of view “an outright crime,” excluded commitments from his model of science, and avoided binding ties in his professional life.²³ The next chapter will argue that commitments are unavoidable, detail their specific form, and outline how they harden over time.

Nor can people seize the upside of turbulence by ignoring the provisional nature of knowledge. All mental maps are static representations of a shifting situation, simplifications of a complex world made without the benefit of knowledge that will only emerge in the future. They remain always and everywhere provisional, subject to revision or rejection in light of new information. The paradox of the map demands a delicate balance between commitment and revision, stability and flexibility. Striking the balance is difficult, but possible, and chapters 5 through 11 of this book suggest practical steps to help strike this balance.