On Chance and Intelligence

How much of our success can we chalk up to innate ability, and how much to random luck?

By Carlos Fuentes


“The road to success and the road to failure are almost exactly the same”    

—Colin R. Davis

Little attention is given to the role that chance plays in business and personal lives. Generally, those who are successful ascribe their accomplishments to personal qualities whereas those who fail see external, uncontrollable factors as the forces that prevented them from achieving their goals. These views are oversimplifications, often misleading. It is certainly not true that discipline, perseverance, planning, intelligence, and talent guarantee triumphs, although they make them more likely. Conversely, individuals who lack these traits sometimes are successful. This is a fact of life borne by observation. In War and Peace, Nikolai Rostov is dismayed when he painfully realizes that the gifts of fortuna can elevate mediocrity—at best randomly, at worst unfairly:

“Sire, I ask your permission to present the Legion of Honor to the bravest of your soldiers,” said [Napoleon’s] sharp, precise voice, articulating every letter.

[…] “To whom shall it be given?” the Emperor Alexander asked Kozlovski.

“To whomever Your Majesty commands.”

The Emperor knit his brows with dissatisfaction and, glancing back, remarked: “But we must give him an answer.”

[…] “Lazarev!” the colonel called, with a frown, and Lazarev, the first soldier in the rank, stepped briskly forward.

[…] It was as if Napoleon knew that it was only necessary for his hand to deign to touch that soldier’s breast for the soldier to be forever happy, rewarded, and distinguished from everyone else in the world.

[…] Russian and French officers embraced him, congratulated him. […] Crowds of officers and civilians drew near merely to see him.

“What do you think of the treat […] all on silver plate? […] What luck of Lazarev! Twelve hundred francs’ pension for life.”

* * *

The favorable influence of intelligence is acknowledged by military thinkers and businesspeople alike. But the role of chance, although accepted by the former, tends to be downplayed by the latter.

The purpose of this article is to examine the subject of chance and intelligence in the corporate and personal settings by:

  1. Laying out their strategic foundations through a brief review of the relevant aspects of Thucydides’ masterpiece, The Peloponnesian War,1 a canonical text in military academies, universities with programs in management, strategy and diplomacy,2 and required reading for entrepreneurs and executives;
  2. Understanding the root causes of misconceptions on success and failure by examining the findings of pop success/strategy research against a statistical background; and
  3. Giving real-world examples of situations that illustrate the interplay between chance and intelligence.

Pondering the roles of chance and intelligence affects how we perceive ourselves and how we see others: Is our wealth the result of hard work and careful planning? Does competition eliminate poor performers and reward winners? Should social benefits be reduced to avoid rewarding the non-deserving? There may be multiple or no answers. Disagreement is certain. Nonetheless, thinking about the subject is time well spent because the implications of our perceptions have far-reaching consequences in our personal lives and in society at large.

Thucydides and The Peloponnesian War

“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”    

—Albert Einstein

Thucydides (460 BCE to 400 BCE) is considered by many the most influential historian of all time. The principal reason for his unique position in Western historiography is the powerful intellect he brought to the writing of history and the sweep of the vision that informs his work. He has a sharp eye for pretenses of all sorts and is skeptical about posturing in the name of virtue. His writing style is authoritative and endowed with unmatched elegance.

The Greeks of Thucydides’ time lived mostly in independent city-states scattered over mainland Greece, the islands of the Aegean Sea, the Ionian coast of Asia Minor, its offshore islands, Sicily, and Southern Italy. Often, one city was in rivalry or at war with another.

In the later sixth century BCE, the reformer Cleisthenes (570 BCE to 508 BCE) initiated political changes that made Athens first into a democracy and then the hegemon of an alliance of city-states. One of its essential principles adopted in Athens was the rule of law and equality before the law for free men.3 In contrast to Athens, Sparta was a strict oligarchy. Its citizens were a small exclusive warrior caste that ruled over a large enslaved indigenous peasant population known as helots. Separated from their mothers at the age of seven, boys were reared separately for 14 years in a system of severe military training.

In the course of the late sixth and the fifth centuries BCE, Athens and Sparta rose to ascendancy over the other Greek cities. While Sparta became Greece’s land power, Athens emerged as Greece’s naval power with a vigorous economy based on trade. As a rule, Athenian policy favored the overthrow of oligarchies in its allied cities and support of the democratic factions, whereas Sparta imposed friendly oligarchies whenever possible.4

The outlooks of the Athenians and Spartans were shaped to a great extent by their views on chance and intelligence. Whereas Athenians and their most important leader, Pericles,5 were the exponents of intelligence, especially in the sense of intelligent policy, the Spartans granted chance a wider scope than the Athenians did. In due course, Spartan leadership came into conflict with Athens’ expansionist ambitions aimed at conquests in mainland Greece. A full-scale conflict broke out in 431 BCE that ended in 405 BCE with the Athenian unconditional surrender to Sparta.

Techne,6 Gnome,7 and Tyche8 in Thucydides

“On what slender threads do life and fortune hang… !” 

—The Count of Monte Cristo, Alexandre Dumas

Intelligence, as understood in this article, is the general rubric for the complex of notions implied by the Greek words techne and gnome—perception, foresight, planning, technical competence, resolve and the like. Chance is the translation of tyche. According to Thucydides, the Athenians believed that although intelligence does not guarantee success, it is the best tool to attain it. The Spartans also had a high regard for intelligence but in their view, chance plays the central role in human affairs.

The Athenian View of Chance and Intelligence

“A goal without a plan is just a wish.”    

—Antoine de Saint-Exupéry

The introduction to the first speech of Pericles contains the gist of Thucydides’ characterization of Pericles as statesman and as political thinker:

I recognize that the spirit which persuades men to go to war can change when the action is on them, and that resolution varies with fortune. … Events can take as stupid a course as human designs: that is why we blame chance for all that runs counter to our calculations… 

This fragment shows that intelligence is the basis of Pericles’ military strategy, which can be characterized as policy based on reason. Such a policy requires the constancy that, he understands, belongs to the intellectual aristocracy, not the common person whose acts are swayed by emotion.9

Pericles describes adversity in terms of human planning, thus connecting chance with planning: Adverse luck is that which was unplanned, badly planned, or contrary to plan. Chance is an objective force that stems from human error but amenable to some control by human reason. With his interpretation of chance, Pericles echoes the views of Democritus,10 who believed that “men have fashioned an image of chance as an excuse for their own stupidity. For chance rarely conflicts with intelligence, and most things in life can be set in order by an intelligent sharp sightedness.”11

Pericles tends to think that the Athenians are more intelligent than the Spartans. The Periclean policy is based on an analysis of the difference between Athens and Sparta.12,13 The Spartan point of view, however, is that men are generally equal in understanding. The Spartans have a single, simple policy that they would presumably always apply against any enemy and that follows from their view of the general equality of men in respect to intelligence.

In short, the Athenians held the faculty of intelligence, judgment, and foresight in the highest regard and considered these qualities to be indispensable in a leader and statesman. The Spartans prefer the gifts of chance, which Pericles scorns.

The Spartan View of Chance and Intelligence

 “Oh, I am fortune’s fool!”     

—Romeo and Juliet, William Shakespeare

As described in the previous section, Pericles is the proponent of intelligence, especially in the senses of intelligent policy. The Spartans, too, think in terms of the chance-intelligence antithesis, but they grant chance a wider scope than does Pericles, and they mean by intelligence a tenacious adherence to their traditional ways. This confidence—in their traditional ways and, by extension, in their constitution and in their community—makes the Spartans, according to their Corinthian14 allies, moderate but also ignorant of the outside world:15

[The Athenians] are revolutionaries, quick with new ideas and quick to put their thoughts into action; you are conservatives, keeping things as they are with no initiative and incapable of action even on the bare essentials. Again, they dare beyond their means, take risks defying judgement, and stay confident in adversity; whereas your way is to act short of your power, diffident even in the strengths of your policy, and convinced that there is no escape from adversity. … For them, uniquely, in any project hoping and having are the same thing, so quickly does action follow thought. This is their lifelong labor, a constant round of work and risk.

Archidamus16 defends the Spartan ignorance and conservatism as not distinct from, but rather an aspect of, moderation and virtue. He argues that the Spartan delay17 provides more security against chance. Archidamus insists that the virtue of soundness of judgment comes from the Spartan education, which teaches strict obedience to the laws, a contempt for useless cleverness, a healthy respect for the enemy, sound preparation for war, and the belief that “we are not schooled in that useless over-intelligence which can make a brilliant verbal attack on the enemies’ plans but fail to match it in consequent action. Rather we are taught to believe that other people’s minds are similar to ours, and that no theory can determine the accidents of chance.”18 Archidamus continues by saying that “it is always our principle to make practical plans on the assumption of an intelligent enemy, and not to let our hopes reside in the likelihood of his mistakes, but in the security of our own precautions.”

The Corinthians speak of the danger of elation inspired by good luck in war: “[In view of their current good fortune, the Athenians] expected no reverses, but achievement alike of the possible and the near impossible. … The reason was the success, beyond any rational prediction, of most of their operations, and this had fueled their hope.”19

In the same way that the Athenian restlessness is related to technical innovation, so, according to Archidamus’ analysis, Spartan sluggishness is related to a sense of a general limitation imposed on human intelligence by the power of chance. For the Spartans, sound judgment is traced ultimately to deference to chance. For Athenians, sound judgment means defiance of chance in the name of intelligence.

Bravery counts for more than experience and understanding; without bravery no technical skill can stand up against danger. As a matter of fact, the Spartans conceive intelligence as resolution or courage.20 Intelligence, as rational judgment, has little meaning for them because they are so impressed by the power of chance. For the Spartans it is a foregone conclusion that chance will overcome intelligence. They counteract chance with a stubborn resistance, an unwillingness to give up.

Diodotus,21 an Athenian commander, summarized the Spartan view on fortune and intelligence thus:

Mistakes, individual or collective, are in human nature, and no law will prevent them. … Poverty, power and the other conditions of life which hold men in the grip of particular passions drive them with an irresistible and overmastering force into dangerous risks. Hope and desire are always ingredients. Where desire leads, hope follows; desire develops the plan, and hope suggests that fortune will be generous; and both are ruinous, as their invisible influence is more powerful than the dangers in plain sight. And fortune does indeed add no less a contribution to the heady mix. Sometimes it presents itself as an unexpected ally, encouraging a man to take risks even from an inferior position.22

Chance and Intelligence in Business Performance

“There are three kinds of lies: lies, damned lies, and statistics.”        

—Benjamin Disraeli

Are Thucydides’ musings on chance and intelligence applicable to businesses in the 21st century? Can we learn from the best and discover a list of principles that are capable of taming fortuna—the magic formula? This is the premise of pop strategy/success books such as From Good to Great, in which author Jim Collins distills lessons from companies that outperformed competitors and the stock market over periods that span several years. Their methodology is as follows:

  1. Categorize companies based on performance. Figure 1, not taken from any pop success/strategy book but similar to many presented in them, shows the shareholders’ returns attained by the top two firms, a poor performer, and the average firm in a universe of 100 companies over a 20-year period. To facilitate comparisons, the returns are normalized at year zero.
  2. Find out how winners attain excellence. Occasionally, study losers to uncover traps to avoid.

Each study finds its own magic formula but it typically includes precepts such as focusing narrowly on core capabilities, diversifying, integrating horizontally, integrating vertically,23 outsourcing certain functions, improving quality, reducing costs, issuing more equity, repurchasing shares, finding uncontested markets (“blue oceans”24), becoming the first adopter of new technologies, avoiding the mistakes made by first-movers, innovating, etc. Because management style is of the greatest significance, victors are asked to identify the leadership traits that set them apart. Typically, their feedback runs along the following lines: believing in yourself, following your passions, taking risks, working hard, being honest, fostering the drive to win, being a team player, caring for employees, not tolerating lukewarm performance, etc. Although it is assumed that poor performers lack strategic vision, grit, discipline, and maybe even a moral compass, they probably disagree with this characterization. It doesn’t matter because their voices are seldom heard.

Many will assert that whether we find the advice of pop success/strategy studies plausible or not, the fact remains that some companies are well managed whereas others are not, as attested by their financial performance. Numbers don’t lie. We can excuse the Spartans for their deference to chance; after all, they had no exposure to the mechanisms of financial markets or modern management theory. It turns out that although they were not schooled in random walk analysis either, they did understand its key element: randomness. The four lines of normalized returns in Figure 1 are the output of random walk model. This means that:

  • The performance depicted in the chart is the result of chance and chance alone; and
  • The track record of most outstanding companies is no more than false positives.25

In short: We are led to attribute, post facto, success to individual abilities (special causes26) when performance is the result of system attributes (common causes27). Thus, the magic formulas discovered by pop strategy/success books are a combination of (i) attributes chosen at random within the context of their study, and (ii) idiosyncratic explanations based on the authors’ beliefs. Not that preconceptions are necessarily bad (who would argue against the benefits of producing high-quality work?), but rather that pronouncements of this type hardly require any research and, in some cases, (e.g., giving honest feedback to one’s boss) may not be the best advice in the real world. Moreover, the fact that reality is vastly more complex than the output of a random-walk model grants chance an even more exalted role, further complicating the task of distinguishing between luck and merit because the differences become exceedingly subtle.

With these considerations in mind, we then ask: What is the probability that by mere luck one company will outperform competitors? To answer this question, two fundamental problems must be solved: distinguishing between common and special causes, and correcting for false positives.

Looking a bit deeper into these issues can be illuminating. First, the most common measure of performance and the metric typically adopted in pop strategy/success books—total shareholders’ returns (TSR)—is inadequate for our purposes, because it depends on the capital market’s estimate of future performance. Whereas the market is a good thermometer of the herd mentality, it is not an indicator of excellence in leadership. Furthermore, TSR looks at the future, not at the past—that is, TSR pays little attention to the actions that led to present success. In order to assess the track record of management, it is better to examine operating measures of performance such as efficiency ratios, current ratios, asset turnover, etc. Return on assets (ROA) is a solid choice because it is generally available and can be measured with reasonable confidence.

Second, each company’s performance depends on peer performance, because rankings are based on comparisons. A ROA of 10% by itself becomes meaningless unless the performance of others is known.

Third, companies must be grouped by types of industry to isolate structural characteristics from management ability. For example, the ROA is low for claims administration companies but large for consulting companies. Other groupings are necessary to remove the effects of firm size, economic cycle, financial structure, etc.

Fourth, correcting for false positives can be challenging and typically requires a substantial amount of data. Removing false positives increases confidence in the results but reduces the number of companies that otherwise would qualify as high performers. It remains an interesting psychological phenomenon to witness how basic statistical principles are bypassed when making judgments about managerial ability.

In conclusion, pronouncements with universal or nearly universal applicability such as “hire the best person for the job” or “don’t quit college” are useful but do not require statistical studies or endorsements by winners. There is no unique strategy that all successful enterprises follow because any sensible course of action depends on the circumstances of the moment. Furthermore, companies often face situations shrouded in so much uncertainty that they must adapt constantly and take their chances. Strange as it may sound, complexity makes leadership more, not less, valuable—but only if it is understood as the ability to harmonize strategic thinking, soft skills, risk-taking, and decisiveness of action.

Chance and Intelligence on Wall Street

“All models have faults—that doesn’t mean you can’t use them as tools for making decisions.”       

—Myron Scholes

The eminent economist John Maynard Keynes28 asserted that many probabilities (including some that arise from economic and actuarial phenomena) are, for practical purposes, not measurable.29 This opinion—a fact, in my view—is not shared by those who profess faith in the Black-Scholes-Merton model and in other financial/actuarial constructs.

In 1994, Myron Scholes30 and Robert Merton,31 among others, managed a hedge fund company called Long-Term Capital Management. They seemed to have the winning formula with their work on derivatives, which earned them the Nobel Prize in economics in 1997. Yet, even in the area of high finance the limitation imposed on human intelligence by the fortuna (the Spartan view) and theoretical errors (the Athenian view) played a role. A year later, Long-Term Capital Management lost $4.6 billion due to its inability to find the safe and lucrative trading strategy promised by their sophisticated models.

Chance and Intelligence in Social Insurance

“There is an inverse relationship between reliance on the state and self-reliance.”     

—William F. Buckley Jr.

Some facts are evident to the point of becoming unnoticed, yet they can be disputed. One of them is the development of national ideologies, a system of beliefs that a group of people finds evident while others do not. In this respect Americans have strong views about liberty, equality, and self-reliance. Admired by many, the “Marlboro Man”32 became a fitting embodiment of the American conception of ruggedness and self-reliance. Closely related to it is the “American Dream,” the belief that anyone, regardless of social status and handicaps, can succeed. Those who believe that self-reliance plays a prominent role in human affairs conclude that fairness dictates that rewards should be commensurate with individual sacrifice because hard work is commensurate with success. Whereas most sensible people agree that rewards ought to be commensurate with sacrifice, some argue that the link between merit and achievement is weak. Thus, someone who believes in self-reliance and the “American Dream” is likely to oppose social insurance on the grounds that taking from a hard-working group to give to an idle one is unfair and perpetuates a state of dependency that is injurious to everybody. She who believes that fortuna controls the socioeconomic rankings of individuals can be expected to support social insurance because on the one hand, being wealthy or being poor is matter settled mostly by uncontrollable forces, and on the other, inequality amplified by institutions causes great damage to its members. Most opinions lie between these extremes.

The point is that our convictions about chance and intelligence have a profound impact on certain fundamental aspects of society. Beliefs (correct or incorrect) and feelings (elevated or base) lead to action more frequently than logical arguments. They are ubiquitous but seldom part of the “scientific” economic discourse because in our times the most common view of economics revolves around assumptions of rationality. Beliefs and feelings play a prominent role in decisions about Social Security benefits. They have influenced the debate about universal health care although their existence has seldom been acknowledged.33

A Case Study: Microsoft

“…the record shows I took the blows and did it my way.”      

—Paul Anka

By all accounts, Microsoft is a success story. A startup with a brilliant idea and a group of talented, motivated, hardworking entrepreneurs so focused that in hindsight they were destined to greatness. Or were they?

Bill Gates’ socioeconomic background gave him access to computers and to the world of programing at a time when almost nobody enjoyed that privilege. He was a student at an Ivy League institution where he became exposed to cutting-edge ideas and where he developed an outstanding network. Thanks to his mother’s connections with IBM’s top management, then the leading computer manufacturer in the world, he signed a contract under which IBM agreed to include the Microsoft operating system in all the PCs it sold. Furthermore, IBM relinquished any claim to exclusivity when it could have easily insisted on it. Signing this amazing contract with IBM, in turn, required other lucky breaks: First, the negotiation for the acquisition of an operating system between IBM and Digital Research (DR) fell at the last minute, thus opening the door to Microsoft thanks to the relationship between Gates and DR’s Gary Kildall. When IBM and Microsoft discussed the operating system, Microsoft had not fully developed one yet. Instead, Paul Allen,34 co-founder of Microsoft, acquired it in 1980 from Seattle Computer Products (SCP) at a low price—SCP was unaware of the purpose of the purchase, otherwise it could have insisted on better terms. Microsoft tweaked SCP’s operating system known as QDOS (Quick and Dirty Operating System) and rebranded it as DOS (Disk Operating System).

There are other factors that in combination with luck explain Gates’ success: his intelligence, his interest as an adolescent to learn about computers, the countless hours he worked, his negotiating abilities, his willingness to take risks,35 his aggressiveness in litigation, his marketing competence, his talent, the high caliber of his partners and employees, etc. But many other companies that end up failing have no less gifted and hardworking founders and employees.

Who would have thought that one of the best decisions in Gates’ life was to drop out of Harvard, thus limiting his academic credentials to a high school diploma? By embracing chance and intelligence à la Athenian, fortuna bestowed on Bill Gates the kind of success that caution can never attain. Context, luck, timing, and foresight combined with ability, hard work, and grit make all the difference.

The Actuarial Profession Under the American Credentialing System

“The big secret in life is that there is no big secret. Whatever your goal, you can get there if you’re willing to work.”   

—Oprah Winfrey

Let me take some liberties as I ponder the roles of merit and luck in the actuarial profession. Before 1990, most credentialed actuaries could expect a successful career. Unemployment was minimal, the work environment stable, there was no competition from other professions, the demand for actuaries exceeded the supply. The link between exam progress (arguably a proxy of expertise) and professional attainment was strong.

In the past several years, the supply of actuaries has grown quickly. Here are some statistics:

  • In 1973, the number of fellows and associates of the Society of Actuaries (SOA) was about 4,300.36 The U.S. population was 212 million. There were 20.3 actuaries per million people.
  • In 1983, the number of actuaries in the SOA directory was about 13,000.37 The U.S. population was 234 million. There were 55.6 actuaries per million people.
  • In 2019, the number of SOA actuaries was about 30,000. The U.S. population was 329 million. There were 91.2 actuaries per million people.

The unemployment endured by some actuaries in the past two decades suggests that demand has not kept pace with supply. This means that wages, although still good, ought to have been affected by the new equilibrium between supply and demand. Furthermore, the work environment is not as stable as it once was, and most actuaries can expect to labor in multiple companies during their careers. The correlation between credentials and professional success is not as strong as it once was. The explanation is not that actuaries practicing in the 1970s were more productive and hardworking than actuaries practicing today, but rather the result of common causes. These include the shorter time for credentialing38 the high number of candidates that desire to become actuaries, the growth of actuarial majors in universities, other professions encroaching in what used to be the exclusive realm of actuarial practice,39 what the business community values in employees, perceptions about actuaries’40 adoption of technology, etc.

Moreover, many talented individuals never had, and will never have, a chance to qualify as associates of fellows due to war, poverty, poor health, language barriers, place of residence, gender, cultural environment, etc. It would be disingenuous to pretend that those who possess the ability but lack the opportunity can overcome the overwhelming obstacles they face by believing in themselves and working hard—these conditions are necessary but not sufficient. To be sure, there are exceptions, but their existence can almost always be explained as random variations—fortuna, if you will, that is, the tail end of a probabilistic distribution—even if these exceptions are portrayed as proof that will of power can conquer anything. In this respect both Athenians and Spartans would disagree with the popular view of success.

Concluding Remarks

“Luck is not something you can mention in the presence of self-made men.”           

—E.B. White

An understanding of how chance and intelligence affect our lives places achievements and failures in context. It changes how we perceive ourselves, others, and society. It helps entrepreneurs come to terms with the risks they assume and their consequences. It can guide our strategic thinking, thus improving the chances of winning. It can influence social policy and the destiny of a country.

The U.S. is beginning to grapple with how to overcome decades, even centuries, of systematic inequality that are the result of exogenous factors such as race, gender, sexual orientation. These uncontrollable factors—elements of chance—carry a significant weight in our lives.  Although some will disagree, it is folly to pretend that the playing field is level.

But back to the dilemma of our article. Niccolò Machiavelli summarized the roles of chance and intelligence masterfully: “Without the opportunity their [notable princes’] strength of mind would have been vain, and without that strength the opportunity would have been lost. … [I]t may be true that fortuna governs half of our actions, but that even so she leaves the other half more or less in our power to control.41     

CARLOS FUENTES, MAAA, FSA, FCA, MBA, MS, is president of Axiom Actuarial Consulting. He can be reached at carlos-fuentes@axiom-actuarial.com.

Disclosure. The opinions expressed in this article are the sole responsibility of the author. They do not express the official views of the American Academy of Actuaries, nor do they necessarily reflect the opinions of the Academy’s officers, members, or staff.


  1. Quotes in this article are from The Peloponnesian War, Thucydides, Oxford World’s Classics, translation by Martin Hammond, 2009.
  2. History can give strategists a keener appreciation of what is possible to do, but also of what must be avoided and what needs to be changed. In this spirit, the very first required reading in the syllabus of Yale’s Program in Grand Strategy is Thucydides’ The Peloponnesian War. The syllabus also includes Niccolò Machiavelli’s The Prince, and the “Federalist Papers.”
  3. The practice of slavery was widespread in ancient Greece. Slaves had no rights. Women had fewer rights than men.
  4. Note the parallel Athens—USA, Sparta—USSR, and now Sparta—China.
  5. Pericles (495 BCE to 429 Athens) was a statesman largely responsible for the development in the later fifth century BCE of both the Athenian democracy and the Athenian empire, making Athens the political and cultural focus of Greece. He led Athens during the first two years of the Peloponnesian War before succumbing to the plague.
  6. In “The Nicomachean Ethics,” Aristotle (384 BCE to 322 BCE) describes three approaches to knowledge: Episteme (scientific knowledge acquired through musing), Techne (practical skill and the systematic knowledge which underlies it), and Phronesis (wisdom acquired through practical action).
  7. A combination of intelligence, planning, and resolve.
  8. Tyche was the Greek goddess of chance, fame, and fortune. She represented the positive and negative aspects of these characteristics and was depicted as carrying a cornucopia (horn of plenty), a ship’s rudder, and the wheel of fortune. The Roman equivalent of Tyche was Fortuna.
  9. It is instructive to contrast Pericles’ view of human nature with the economic hypothesis of rational expectations. See “On Economics: First Principles,” Contingencies, July/August 2020.
  10. Democritus (460 BCE to 370 BCE) was a central figure in the development of philosophical atomism.
  11. https://en.wikiquote.org/wiki/Democritus.
  12. The Peloponnesian War, 1.140 (chapter 1, section 140).
  13. Pericles’ investigation of Athens’ and Sparta’s strengths and weaknesses is a proto SWAT analysis. See “The Connection Between Military and Business Strategies,” Contingencies, May/June 2015.
  14. Corinth is an ancient city in south-central Greece. In 550 BCE an oligarchical government seized power and made Corinth a member of the Peloponnesian League. Corinth participated in the Persian Wars and Peloponnesian War as a Spartan ally.
  15. The Peloponnesian War, 1:70.
  16. Archidamus was a Spartan king who reigned from 476 BCE until his death in 427 BCE.
  17. The modern strategic equivalent is real options. See “Strategy as a Portfolio of Real Options,” Harvard Business Review, Jul/Aug 1988. See also “Demystifying the Art of War,” Contingencies, January/February 2019, in connection with speedy or delayed war strategies.
  18. The Peloponnesian War, 1:84.
  19. The Peloponnesian War, 4:65.
  20. This assertion is forced in English but flows naturally in Greek. See the section “Techne, Gnome, and Tyche in Thucydides” above.
  21. Diodotus appears only once in The Peloponnesian War. He was a member of the Aristocratic (pro-Pericles) Party and commanded the garrison of Chalcis. In 427 BCE, he opposed Cleon’s proposal to kill the adult male population of Mytilene and enslave the women and children.
  22. The Peloponnesian War, 3:45.
  23. Horizontal integration is the process of acquiring or merging with competitors, leading to industry consolidation. Vertical integration is the combination in one company of two or more stages of production normally operated by separate companies.
  24. See “The Connection Between Military and Business Strategies,” Contingencies, May/June 2015.
  25. A test result that incorrectly indicates that a condition or attribute is present.
  26. The term “special causes of variance” refers to unusual, nonquantifiable variations in a system. From the probabilistic point of view, they are unpredictable and nonquantifiable.
  27. The term “common causes of variance,” also known as “noise” or “random cause,” refers to quantifiable and historical variations in a system that are natural. From the probabilistic point of view, they are ongoing, consistent, and predictable.
  28. John Maynard Keynes (1883–1946) was a British economist, political activist, and successful investor. He created macroeconomics.
  29. For example, what is the probability that civil engineering will be the 17th-most popular field among engineers in 2040? “A Treatise on Probability,” John Maynard Keynes (1921).
  30. Myron Samuel Scholes (1941–) is a Canadian-American financial economist and professor at the Stanford Graduate School of Business.
  31. Robert Cox Merton (1944–) is an American economist and professor at the MIT Sloan School of Management.
  32. The Marlboro Man was one of the most successful advertisement campaigns of all time. It ran in the U.S. from 1954 to 1999. Five men who appeared in the advertisements died of smoking-related diseases.
  33. Another important factor that is frequently neglected in policymaking is the racial composition of countries at the time when their social security systems were created. This idea will be developed in a future article.
  34. Paul Allen and Bill Gates were childhood friends. During his tenure as programmer at Honeywell in Boston, Allen, a high school dropout, convinced Gates to leave Harvard to create Microsoft, which they did in 1975. Allen left active operations at Microsoft in early 1983 after being diagnosed with Hodgkin’s lymphoma. He passed away in 2018 at age 65.
  35. Taking risks leverages the payoffs but creates uncertainty in the outcomes. When the outcome is a “win,” we are prone to equate risk with success. We tend to be sympathetic to those who take chances and succeed.
  36. See “The Future of the Actuarial Profession as Viewed in AD 1974,” Transactions of the Society of Actuaries (1974), by John M Bragg, past president of the Society of Actuaries, p. 545. See also “A Reflection on Jack Bragg’s ‘The Future of the Actuarial Profession,’” Innovators & Entrepreneurs, August 2017, by Mark Spong and Brittany Lee.
  37. See “Interview with Dave Spencer” in Innovators & Entrepreneurs, May 2015.
  38. For the opinion of Milton Friedman (1976 Nobel Laureate in economics) about the actuarial exams of the 1970s and his record when he took them, see the video clip “Milton Friedman Wanted to Become an Actuary,” available on YouTube.
  39. See “New Years’ Evolution,” Innovators & Entrepreneurs, February 2014, by Patrick Chaaya for reflections about the actuarial profession.
  40. See “Leadership and Development: Where Do We Go Now?” The Stepping Stone, November 2019, by Mitchell Stephenson.
  41. The Prince, Niccolò Machiavelli, Norton Critical Edition (1972), p. 16.
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