- The tantalizing and compelling pursuit of mathematical problems offers mental absorption, peace of mind amid endless challenges, repose in activity, battle without conflict, refuge from the goading urgency of contingent happenings, and the sort of beauty changeless mountains present to senses tried by the present-day kaleidoscope of events.[Morris Kline, Mathematics in Western Culture (Oxford University Press, 1953), 470.]
Take chances occasionally. It is essential to growth and development.
When my son was a boy, we ate at an Ethiopian restaurant. On the table were small green elongated peppers. Not being familiar with them, he decided to try one. His mother cautioned him that they might be too hot, to which he replied “Well, Mom, sometimes you just have to take chances.” He soon regretted the decision.
Psychologists are hard at work trying to understand the foundations and implications of risk-taking. Birth order does not appear to affect it but economic inequality does. Factors related to risk-taking include “self-regulation, self-control, executive functioning, effortful control, cognitive control, impulsivity, . . . and inhibition . . .“. . . relative deprivation may be a source of information that individuals use to update their belief and change their behavior.” “Relief from incidental fear evokes exuberant risk-taking”. Depletion of self-control resources (ego depletion) does not appear to affect it. Drug and alcohol consumption do appear to affect it, along some parameters. Prefrontal cortex monitoring suggests that “heterogeneity in risk-taking behavior can be traced back to differences in the basic physiology of decision-makers’ brains”.
“Humans adapt their risk-taking behavior on the basis of perceptions of safety”. For example, bicycle riders tend to take more risks when wearing a helmet than when not. That female sexual behavior varies across the ovulatory cycle seems like an obvious point. “Night owl women are similar to men in their relationship orientation, risk-taking propensities, and cortisol levels”.
Psychopathologies may lead to unwise risk-taking. For example, “ADHD-associated risk taking is linked to exaggerated views of the benefits of positive outcomes.”
Gaps related to risk-taking include a gap between description and experience, a gap between behavior and self-report of behavior, and a gap over time. Professionals, such as surgeons, are routinely called upon to decide which risks are reasonable and which are not. In most people, decisions to take or not take risks vary with the complexity of the options presented, to such an extent that calculation of adaptive versus unreasonable risk can be like a crap shoot. People are more inclined toward risk when listening to music they like than when listening to music they do not like. However, intelligence does play a positive role in favor of adaptive risk-taking, including in adolescence. Cognitive impairments can affect judgment, leading to an increased willingness to undergo medical treatments.
Economic risk-taking is a subject of extensive study. Many behavioral phenomena are relevant. In many cultures, especially in the “developed” world, it is celebrated, and systems of laws are devised to encourage it. Investment behavior tracks certain profiles associated with risk-taking. Our consumer culture appears to have redefined “humans’ self-control ability”. Economic forecasting appears to have predictable effects on economic risk-taking. Testosterone appears to be a factor in financial market behavior and performance, a finding that business schools may see as an important subject of their curricula. However, both “(L)ow- and high-testosterone individuals exhibit decreased aversion to economic risk”. “Cortisol and testosterone increase financial risk taking and may destabilize markets”. However, if enough money is to be made first, many investors may not care. At least one study has demonstrated “a non-linear inverted U-shaped relationship between corporate governance and firms’ investment risk”.
No mathematical model or precise rule has been or perhaps can be developed to distinguish between useful and non-useful risk-taking, perhaps for the obvious reason that taking a risk necessitates an approach to the unknown. Good risk-takers generally employ good judgment. Foolish risk-takers do not. A well-considered and well-structured system of values we can help us to understand the difference. Yet because we must take risks in order to grow, we begin to take them long before we know how to take them wisely. Another departure in our approach is that we do not presume that a perfect system of ethics is possible. This may seem like an obvious point but we Humanists are often challenged on our ethical belief systems by theists whose challenges imply or suggest that theirs is a perfect system. Because theistic models dominate most cultures, we offer this as a departure from conventional norms.
Our model proposes and advocates adaptive risk-taking, which is based on a reasoned assessment of the likely benefits of risk-taking behaviors. A balloon analogue risk task (BART), which assesses the interplay between risk-taking and inhibitory control, can be used to measure “advantageous and disadvantageous risk-taking” (see also here). White matter development in the brain and corresponding degrees of working memory appear to be related to these processes. (My son had no working memory of biting into a hot pepper, until he did.) Risk-taking propensity can change significantly over a lifetime and “across different domains of life”. It may have genetic foundations. “Older adults are more risk avoidant” than younger people. No surprise, risk-taking behavior can reach a peak during adolescence, due to factors including “lack of control (and) “excessive sensitivity to immediate rewards”. Impulsivity appears to follow a predictable pattern over most lifetimes (see also here) (see also this international survey). Strategies can be devised to “protect against risk-taking behaviours among adolescents”.
Risk-taking is critical to adolescents as they “venture out into the world, learn about their limits, and form social identities separate from their families, paving the way for independence.” A capacity for quick thinking is positively associated with some kinds of risk-taking. Risk-taking appears to be positively associated with creativity only in the social domain but not in financial, health and safety, recreational or ethical domains. Musicians may seek to play perfectly but they must also take risks musically in order to give a satisfying performance.
This distinction between all risk-taking and the narrower category of adaptive risk-taking is one of many such distinctions in our model. Some of these distinctions will pivot on a sharp contrast, others on a nuance. Others, such as this distinction of adaptive risk-taking is a clarification, because most people recognize the difference – and its significance – between taking a full bite out of a blistering hot pepper and cautiously trying a new dish. (My son quickly learned it.) I point out this distinction out to make it clear and explicit, because sometimes we pay too little attention to distinctions that matter, assuming perhaps that they do not.
Challenge yourself. Push yourself beyond your comfort zone. If that becomes your habit, growth and progress will become your habit too.
A substantial portion of adaptive risk-taking concerns the embracing and taking on of challenges. The basketball player Michael Jordan was featured in an advertisement, stating how he had missed many important shots at the basket; his conclusion was “that is why I succeed.” Jordan had a strategy for success: most of its elements were related to embracing personal challenge. Taking on these challenges virtually guarantees that we will experience failure.
Jordan’s strategy has been described as “first learn to fail”. “Failure is a major component of learning anything.” We learn by making mistakes. Some instructors use a “productive failure” model, in which students are set up to fail, as a predicate for learning, growth and development: this has been employed in mathematics education, and analyzed in contrast to “vicarious failure” and “unproductive success”. Design principles have been developed for productive failure in education.
Fear of failure adversely affects student performance and entrepreneurship. It can be transmitted from one generation to another. Fear of success can also inhibit challenge-taking and success. Anxiety tends to inhibit some people but not others.
Personal challenge is essential to growth and development. This has been demonstrated in studies of new doctors and scientists. An “achievement goal framework” has been developed, based on acceptance versus avoidance of challenges. Cross-cultural differences have been identified: for example, in one study, North Americans who failed on a task persisted less on a follow-up task than those who succeeded, while Japanese who failed persisted more than those who succeeded.
Seeking out challenges and taking them on, are essential first steps in personal development. When we challenge ourselves, we set out bravely on life’s journey. Like life, these ideas are invitations. Join us, if you will.
T.E. Lawrence was an epic risk-taker, who left his work as an archaeologist to serve with irregular Arab forces in guerrilla operations against the Ottoman Empire. Perhaps every soldier takes risks that are as great but few have taken them so grandly.
- T.E. Lawrence, Sir Herbert Samuel, Amir Abdullah (April 1921)
Risking in large context:
- Kevin Fong, Extreme Medicine: How Exploration Transformed Medicine in the Twentieth Century (Penguin Press, 2014): on how testing human limits can “spawn medical breakthroughs.”
- Greg Lukianoff and Jonathan Haidt, The Coddling of the American Mind: How Good Intentions and Bad Ideas are Setting Up a Generation for Failure (Penguin Press, 2018): “The book, which expands on a widely circulated 2015 article in The Atlantic, identifies what the authors refer to as ‘the three Great Untruths’ of the current moment: ‘what doesn’t kill you makes you weaker’; ‘always trust your feelings’; ‘life is a battle between good people and evil people.’”
Other true narratives on facing challenges:
- Claire Tomalin, A Life of My Own: A Memoir (Penguin Press, 2018): “Few things were easy for the author.”
- Roman Dial, The Adventurer’s Son: A Memoir (William Morrow, 2020): “Dial raised his son to be an explorer, too. And then his son disappeared.”
- Ben McGrath, Riverman: An American Odyssey (Knopf, 2022): “The true story of Dick Conant, a troubled and charismatic man who disappeared while paddling from New York to Florida.”
Documentary and Educational Films
- T.E. Lawrence, Seven Pillars of Wisdom: A Triumph (1922).
- Robert Louis Stevenson, Treasure Island (1883): the classic adventure novel.
- Andrew Motion, (Crown Publishers, 2012): a contemporary sequel to the classic tale.
- Meg Wolitzer, The Uncoupling: A Novel (Riverhead Books, 2011): in this novel about women who give up sex and find themselves, the “point . . . is the exploration.”
- Derek Palacio, The Mortifications: A Novel (Tim Duggan Books, 2016): “Before the end of the first chapter, this fractured family has fled their native Cuba, leaving behind a country, husband, father and culture, and while their migration to America occurs as part of the Mariel boatlift of 1980, it is also, Palacio suggests, an ancient story — a narrative of exile as old as the Greek tragedies.”
- Nicole Krauss, Forest Dark: A Novel (HarperCollins Publishers, 2017): on the “freedom to fail”
- Chelsey Johnson, Stray City: A Novel (Custom House, 2018): “At its heart, this book is about risk-taking, and Johnson should be admired for taking the ones she does.”
- Claire Vaye Watkins, I Love You But I’ve Chosen Darkness: A Novel (Riverhead Books, 2021): “The narrator of Claire Vaye Watkins’s new novel (also named Claire Vaye Watkins) makes an unholy mess of her carefully constructed life and then has to decide whether she can — or wants to — put any of its parts back together.”
- Bonnie Garmus, Lessons in Chemistry: A Novel (Doubleday, 2022): “Zott ad-libs her way into a role that suits her, treating the creation of a stew or a casserole as a grand experiment to be undertaken with utmost seriousness. Think molecular gastronomy in an era when canned soup reigned supreme. Baked into each episode is a healthy serving of empowerment, with none of the frill we have come to associate with that term.”
Open the links for lists of children’s books on this subject, which is central to child development.
- Frida Kahlo, The Bride Frightened at Seeing Life Opened (1943)
- Salvador Dali, The Feeling of Becoming (1930)
- Ivan Aivazofsky, Icebergs in the Atlantic (1870)
- Frederic Edwin Church, The Icebergs (1861)
- Georges Rouault, Automne (1948)
- René Magritte, The Difficult Crossing (1926)
- Wassily Kandinsky, Tension en hauteur (1924)
- Wassily Kandinsky, Mild Tension (1923)
Music: songs and other short pieces
Film and Stage
- The Lord of the Rings: The Two Towers: Frodo’s companion Sam sums up the message at film’s end, there is good in the world and it’s worth taking risks for.
- The Right Stuff, about American astronauts in the Mercury space program
- Man Hunt: an attempt to assassinate Hitler goes wrong
- Risky Business, about risk from the perspective of a suburban teenage male
- The Secret World of Arietty: a tiny wall-dwelling creature defies convention and danger to engage a larger and more interesting world
- The Little Mermaid: Disney’s altered and animated version of Hans Christian Andersen’s story about a young mermaid who risks everything to become human and pursue human relationships
- Junior Bonner, about a personal challenge
- Fargo, a film by the wickedly funny Coen brothers that tests the limits of the art with a story set in a locale of unimaginative people that “rotates its story through satire, comedy, suspense and violence”
- Babe: “a young pig fights convention to become a sheep dog – or, rather sheep pig”
- Inside Out: an animated film about the inevitably difficult task of personality integration and growth
On the shadow side:
- Pleasantville, an updated version of the fall of man with an explicit lesson: life is colorless without variety and change
Music: Composers, artists, and major works
Frédéric Chopin’s Polonaises challenge the performer, and in tone and theme suggest the distinction of moving forward in the world by challenging ourselves (performances by Rubinstein, Pollini and Ashkenazy).
Ravel’s Gaspard de la Nuit (Gaspard of the Night) (1908) is among the most difficult of piano works to play, and also reflects challenges in life. “. . . the inspiration for Gaspard comes from three poems by Aloysius Bertrand, and the triptych of pieces represents darkness, hallucinations and terrors through the medium of daring, advanced technical devices within a classical three-movement structure.” The three poems are Ondine (Undine), Le Gibet (The Gibbet), and Scarbo.
Sergei Rachmaninoff’s knuckle-busting works challenge the abilities of the most accomplished pianists.
- Rachmaninoff, Piano Concerto No. 1 in F sharp minor, Op. 1 (performances by Richter, Pletnev, Magaloff and Nasserl)
- Rachmaninoff, Piano Concerto No. 4 in G minor, Op. 40 (performances by Rachmaninoff, Michelangeli and Trifonov)
- Rachmaninoff, Rhapsody on a Theme of Paganini, Op. 43 (performances by Smith, Ashkenazy, Fedorova and Matsuev)
Other compositions that challenge the performer:
- Chopin, 4 Scherzos for piano (performances by Rana, Richter, Horowitz and Pletnev)
- Alkan, Grande Sonate, “Les quatre âges” (The Four Ages), Op. 33 (1848)
Other works, in which taking risks and/or challenging the self is a theme:
- Antonín Dvořák, Rusalka: an operatic rendering of Andersen’s “The Little Mermaid” (performances featuring Fleming, Šubrtová and Barker)
- Alexander von Zemlinsky, (The Mermaid), an orchestral version of the same story
- Ensemble Polaris, “Uncharted Waters” album: this charming disc relies on Swedish melodies, instruments and folklore. The casual listener might be fooled into thinking this compilation is just for fun but the intermittently dark musical tones reveal the more serious intent: this music is about encountering the world, with all its attendant risks.
- Laura Elise Schwendinger, High Wire Act
- Landowski, Symphony No. 1, “Jean de la Peur” (1949). A sense of fear pervades this symphony. L. Dietrich expresses its overarching theme: “He who is so small that he cannot even conceive of dread shall remain forever in the corset of his smallness.” The composer explains the work: “A certain type of emotion and situation is to be found, bringing a certain music. A character, by his thoughts, his feeling, his sensibility, calls for a certain musical translation, and a climate in which reminiscences take shape is created naturally.” Landowski summrarizes the first movement, Allegro moderato, as “For born of the mysteries of the world was Fear, which stood and looked at John.” Of the second movement, Allegretto scherzando, the compser offers this: “. . . and Jehab thought to destroy fear in killing the mysteries.” He summarized the Adagio third movement: “. . . but slowly another fear arose, and this fear looked at his from inside.”
- Guridi, Sinfonia Pirenaica (Pyrenean Symphony) (1945): the sound of a grand adventure
- Hindemith, String Quartet No. 4, Op. 22 (1921): evoking a life fraught with difficulties.
- Werner Josten wrote of his composition “Jungle” (1928): “the music tries to portray the emotions and sensations which assail a white man entering the jungle, with its lures, terrors, primitive love and ferocious death.”
- Holmboe, Violin Concerto No. 2, M297, Op. 139 (1979)
- Holmboe, Concerto for Viola, Op. 189 (1992)
- Massenet, Piano Concerto in E-flat Major (1903): the protagonist faces every difficulty, without hesitation.
- Schumann: Cello Concerto in A Minor, Op. 129 (1850)
- Gerber, Symphony No. 1 (1989)
- Gerber, Viola Concerto (1996): movement 1; movements 2 and 3.
- Zumsteeg, Die Geisterinsel (The Tempest) (1798): as in Shakespeare’s play, the characters encounter a brave new world, with more challenges than they anticipated. (Here is the overture.)
- Hoiby, The Tempest (1986): an opera based on the same idea
- Dutilleux, Symphony No. 1 (1951)
- Atterberg, String Quartet No. 3 in D Major, Op. 39 (1937)
- Krenek, String Quartet No. 3, Op. 20 (1923)
- Krenek, String Quartet No. 7, Op. 96 (1944)
- Enescu, Octet for Strings in C Major, Op. 7 (1900)
- Enescu, Piano Quintet in A Minor, Op. 29 (1940)
- Rolón, Piano Concerto with grand orchestra, Op. 42
- Zyman, Piano Concerto
- Nordheim, Spur, for accordion & orchestra (1975)
- Raga Mishra Bhairavi (Misra Bhairavi) (performances by Zia Mohiuddin Dagar and Aashish Khan)
- Hailstork, Symphony No. 2
- Raga Malahari is a Carnatic ragam associationed with the rainy season and performed in early morning (performance by Seshagopalan)
- Balsys, Reflections of the Sea
- Krommer, Symphony No. 7 in G minor, P I:7
- Ķeniņš, Symphony No. 4
- Rózsa, String Trio, Op. 1 (1927)
- Rózsa, String Quartet No. 1, Op. 22 (1950)
- Rózsa, String Quartet No. 2, Op. 38 (1981)
- Wordsworth, Cello Concerto, Op. 73 (1963)
- Robert Simpson, Symphony No. 5 (1972)
- Elena Ruehr, Icarus, for clarinet and string quartet (2017): a tone poem drawn from the Greek legend of the man who flew too close to the sun
- Johann Wilhelm Hertel: Cello Concerto in A Minor (1759)
- Thomas de Hartmann, Concerto for Piano and Orchestra, Op. 61 (1942)
- Nico Muhly, Stranger (2019), a song cycle on the immigrant experience coming to the United States early in the 20th century
- Alexander Hawkins, Mirror Canon, “Break a Vase” (2021), titled after a comment by Saint Lucian poet Derek Walcott on accepting a Nobel Prize: “Break a vase, and the love that reassembles the fragments is stronger than that love which took its symmetry for granted when it was whole.”
The low lands call / I am tempted to answer / They are offering me a free dwelling / Without having to conquer
The massive mountain makes its move / Beckoning me to ascend / A much more difficult path / To get up the slippery bend
I cannot choose both / I have a choice to make \ I must be wise / This will determine my fate
I choose, I choose the mountain / With all its stress and strain / Because only by climbing / Can I rise above the plain
I choose the mountain / And I will never stop climbing / I choose the mountain / And I shall forever be ascending
I choose the mountain
[Howard Simon, “I Choose the Mountain”]
- Wallace Stevens, “Hymn from a Watermelon Pavilion”
- Robert Frost, “A Line-Storm Song”
- Anaïs Nin, “Risk”
- Jorge Luis Borges, “One Morning in 1649”
- Thomas Gray, “Ode on the Death of a Favourite Cat Drowned in a Tub of Goldfishes”