Peak — Secrets from the New Science of Expertise
by Anders Ericsson and Robert Pool
Houghton Mifflin Harcourt, Boston, 216
My Rating: 4/5
How does one become an expert mathematician? How does one become one of the best mathematician’s in the world?
In 2008, New Yorker magazine science writer Malcolm Gladwell popularized an answer in his bestseller Outliers: ten-thousand hours of a special kind of practice called “deliberate practice.” Gladwell, whose father is a mathematics professor, attributed success in essentially all fields to this seemingly simple rule, citing examples including Bill Gates, the Beatles, and theoretical physicist J. Robert Oppenheimer amongst others.
Both in the book and in his book promotion presentations, several of which are available on YouTube, Gladwell cited the research of psychologist K. Anders Ericsson on expert and peak performance. Ericsson coined or at least heavily promoted the phrase “deliberate practice” in academic research. Ericsson indeed attributes expert and peak performance largely to many hours of “deliberate practice,” although not specifically ten-thousand hours. Ericsson and his collaborators have written many scientific research papers and scholarly books on deliberate practice. His work was little known to the general public prior to the publication of Outliers.
Peak — Secrets from the New Science of Expertise is a popular version of Ericsson’s work written with veteran science writer Robert Pool. It is written in a more accessible, lighter, less dry style than Ericsson’s scholarly books and research articles. It discusses his major research projects and results without the extensive, sometimes mind-numbing detail of a scholarly book or research paper. In a number of respects, this is a “self-help” book although the scholarship and level of technical detail is much higher than many self help books.
The Good Points
Peak is clear, well-written, and easy to read. It is an accessible overview of Ericsson’s research and his theories of expert and peak performance with citations to scholarly papers and sources in the detailed end notes. It is an easier read than his scholarly papers and books and probably a better place to start. Peak gives the reader Ericsson’s actual data and opinions direct from the horse’s mouth. He spells out the differences between his actual work and Gladwell’s interpretation in the subsection “No, the Ten-Thousand-Hour Rule isn’t Really a Rule” in Chapter Four: The Gold Standard (pages 109-114 in my copy).
The book and Ericsson’s work in general makes a great case for the critical role of some sort of practice in nearly all cases of expert or best performance. In general, it takes several thousand hours of some sort of practice to reach expert or best performance levels.
A specific kind of practice — heavy practice and drilling of relatively rare moves or situations such as the back-hand in tennis (a favorite example of Ericsson) — appears to be necessary and perhaps the only real requirement for expert or peak performance in some fields such as tennis. At times this fairly specific type of practice appears to be what Ericsson means by deliberate practice.
What is Deliberate Practice?
The major weakness of the book and Ericsson’s work in general is the vague, shifting definition of “deliberate practice.” Ericsson unintentionally gives an example of this problem on page 75 of the book:
For example, when we presented our initial [book] proposal to our agent Elyse Cheney, she and her colleagues had trouble understanding deliberate practice clearly. In particular, they didn’t get what separates deliberate practice from other forms of practice, other than that it is more effective.
Peak takes over three chapters and ninety-six pages to work its way up to actually defining deliberate practice in the subsection “The Principles of Deliberate Practice” in Chapter Four: The Gold Standard (pages 97-100 in my copy). Deliberate practice actually appears to be defined in seven lengthy bullet points on pages 99 (all of the page) and 100 (about half the page).
Many of the bullet points in the definition are quite vague and even don’t always seem to match the examples given in the book. For example, Ericsson emphasizes solitary practice as a characteristic of deliberate practice, but then cites a new freshman physics education program at the University of British Columbia (UBC) that emphasizes breaking the students into collaborative groups as an example of deliberate practice in action.
The vague definition of deliberate practice makes it difficult and perhaps impossible to disprove — falsify in the language of Karl Popper — the thesis that expert performance is a direct, presumably monotonically increasing function of the quantity of deliberate practice, most often measured by hours of practice.
For example, Peak discusses a study that Ericsson and his collaborators did of top violin students at the elite Berlin University of Arts (Universitat der Kunste Berlin). This study divided the students into three groups: ten “good” students, ten “better” students, and ten “best” students as rated by professors at the University. Perhaps not surprisingly, on average the “best” students had more lifetime hours of practice than the “better” who in turn had more lifetime hours of practice than the merely “good” students.
According to Ericsson, Malcolm Gladwell pulled his ten-thousand hour number from this study. On average twenty year old students at the school had ten-thousand hours of “deliberate practice” — Ericsson defined the violin practice as deliberate practice. Note that twenty year old violin students are not professional or world champion violinists yet. In fact, Ericsson notes that professional expert violinists typically have more like twenty-thousand hours of practice under their belt. Ericsson also notes that ten-thousand hours is an average for the twenty year old students; there was significant variation from student to student.
The big problem is that these numbers are averages. Some of the “best” violinists had significantly fewer hours of practice than other of the “best” violinists. Could this in fact be due to some innate aptitude for violin, a concept Ericsson rejects vehemently? Certainly!
In “The Role of Deliberate Practice in Chess Expertise” by Neil Charness, Michael Tuffiash, Ralfe Krampe (one of Ericsson’s collaborators in the violin study), Eyal Reingold, and Ekaterina Vayukova (Applied Cognitive Psychology, Volume 19, pages 151-165 (2005)) the authors find that only forty percent (40 %) of the variance in chess skill ratings, less than half, can be explained by a multivariate linear regression model using hours of practice as one of the variables. It is true that practice is the single largest explanatory variable, but a lot remains unexplained. As I will discuss below, studies of chess play an outsized role in Ericsson and his collaborators research — and in Peak.
Both everyday experience, anecdotal data, and research studies often show substantial unexplained variation in the amount of practice associated with expert or peak performance. This could easily indicate the contribution of innate aptitude, possibly genetic in nature, or some other entirely unidentified factor or factors.
How does Ericsson get around this? It is here that the vague, shifting, plastic definition of deliberate practice comes into play. Perhaps the practice was not all of the same quality. Five thousand hours with a very good teacher or coach might beat seven thousand hours of practice with a merely good teacher or coach. Perhaps the students who needed more practice weren’t always focusing on their practice, a requirement that Ericsson includes in his lengthy definition of deliberate practice:
Deliberate practice is deliberate, that is, it requires a person’s full attention and conscious actions. It isn’t enough to simply follow a teacher’s or coach’s directions. The student must concentrate on the specific goal for his or her practice activity so that adjustments can be made to control practice.
Absent telepathy or a mind-reading machine, there is simply no way to be sure if a person was applying “full attention” to practice. What exactly is the definition of full attention?
Since expert or peak performance in field after field after field is highly correlated with substantial amounts of study and practice — a position very few contest — it is extremely difficult to rule out the deliberate practice theory given the vague definition of the term. One needs to find very rare, very unusual examples of people who perform at an expert or peak level with essentially no or minimal practice, perhaps a few hundred hours of practice at most. The high jumper Donald Thomas from David Epstein’s book The Sports Gene which Ericsson attempts to debunk in Chapter Eight: What about Natural Talent? may be such a rare example. In practice, rare examples can easily be dismissed as flukes or frauds.
The research cited in Peak has a number of methodological weaknesses. Like much research into human beings, it relies heavily on “convenience samples,” in other words people who are easy to recruit into studies, generally undergraduate and graduate students at universities where the researchers live and work. These samples are generally small. Many of the studies cited in the book involve less than one-hundred subjects. The digit memorization study that Ericsson and his collaborators conducted at Carnegie Mellon University involved only three students according to the book: Steve Faloon, Renee Elio, and Dario Donatelli.
Small samples have large statistical errors and are more susceptible to biased sampling, although bias can be a major problem in huge studies with millions of subjects or data points. Students from often elite colleges and universities like Carnegie Mellon are obviously a highly biased sample to start with.
As an aside, the performance of the three subjects in the digit memorization study varied substantially. Steve Faloon and Dario Donatelli performed much better than Renee Elio according to the book, although all three improved with practice. Renee was the only woman in the study and many standardized tests such as the math SAT in the United States and other forms of measurement continue to show that on average women are perform poorer on mathematical tasks than men. Again, the difference in performance between Renee and the two men is inconsistent with the simple deliberate practice theory.
Nearly all the research involves specialized competitive activities such as sports, music and other performing arts, and games such as chess. Chess plays an especially important role in the research which grew out of Ericsson’s mentor Herbert Simon’s research into human cognition through the detailed study of chess.
All of these fields involve short, generally timed or time limited contests or performances. All involve large amounts of time devoted to practice in preparation for these short contests or performances. All of these fields have many decades, even centuries of development. In most cases, the rules and equipment have changed little over the decades or centuries. Many of these fields, notably chess which has played a central role in the research, are heavily male dominated, with few women participating even today.
Although Ericsson is careful to qualify a number of his statements, Ericsson like Malcolm Gladwell in Outliers still endeavors to extrapolate the results of his research on these fields to professions such as medicine and more general business activities.
Deliberate Practice and Mathematics
Cognition and expert/peak performance in chess has been studied extensively by psychologists and others including Adriaan de Groot (a former champion chess player), Ericsson’s mentor Herbert Simon and his collaborator Alan Newell, and many others. Chess is often seen as a highly intellectual activity in which peak performance reflects high intelligence. Thus it has been heavily investigated as a model for other presumably intellectual activities such as scientific research and mathematics. There is much more data and research on chess than on the practice of mathematics.
As Ericsson discusses, this intellectual image of chess is part of our shared popular culture. Movies, television shows, and other art forms often use chess or playing chess to show the deep intellect of characters. The recent movie Sherlock Holmes: A Game of Shadows features a chess game between the hero Sherlock Holmes and his arch-nemesis Professor Moriarty (Moriarty is described as a brilliant mathematician in “The Final Problem” by Arthur Conan Doyle). Chess and chess playing computers play a central role in the short lived science fiction series Terminator: The Sarah Connor Chronicles with the hero John Connor depicted as a chess player and strong hints his ultimate enemy the Skynet supercomputer is derived from a chess-playing computer prototype that appears in the first season. The romantic comedy Penelope goes against the male chess stereotype portraying the eponymous heroine as a chess player easily defeating her suitor in a match.
For those of us interested in mathematics and other quantitative professions, the question has two parts. First, how accurate is the deliberate practice theory of chess? As the article cited above “The Role of Deliberate Practice in Chess Expertise” illustrates, with only forty percent of the variance in chess scores explained by all variables including practice, it is far from clear that deliberate practice provides an adequate theory of performance in chess.
Second, can one extrapolate from studies of chess to mathematics? Chess has a number of similarities to competitive math activities at the high school and college level. According to James Gleick’s biography Genius the theoretical physicist Richard Feynman competed in New York City regional algebra and math contests, winning the city wide contest. He subsequently took the early Putnam Exam in mathematics at MIT, scoring the best of all takers that year.
Fields Medal winning research mathematician Terrence Tao competed in the International Math Olympiad in 1986, 1987, and 1988, winning a bronze, silver, and gold medal. He remains the youngest winner of each of the three medals in the Olympiad’s history, winning the gold medal shortly after his thirteenth birthday. Thus, competitive math activities that resemble chess in a number of ways can clearly be part of the training of a successful research mathematician.
The problem is that research in mathematics, whether basic or applied, differs substantially from short timed contests generally covering known knowledge or methods. The goal of research, including highly applied research for product development, is to come up with something new and generally takes months if not years of effort. Empirically, this effort often involves large amounts of frustrating trial and error. Major discoveries frequently involve mysterious flashes of insight, the “Eureka” or “aha” moment, something that is especially difficult to explain or understand at present.
Some inventors and discoverers like Albert Einstein and his collaborator Marcel Grossman were not as technically proficient in mathematics (or physics) as one might think. Einstein was unable to get into the top physics graduate schools in Europe and ended up getting his Ph.D. at night at the University of Zurich while working as a patent clerk. One of his professors at ETH in Switzerland, Hermann Minkowski, infamously referred to Einstein as “that lazy dog.” David Hilbert easily figured out the equation for General Relativity once Einstein explained the concept to him, whereas Einstein and Grossman struggled with finding the equation, leading to the notorious priority dispute with Hilbert over General Relativity.
One sometimes hears the phrase “it is not a sprint, it is a marathon” to describe some activities. But marathons are only 26.2 miles in length, taking an accomplished runner just a few hours. The current world record time for a marathon, held by Dennis Kimetto of Kenya, is two hours, two seconds, and fifty-seven hundredths of a second (2:02:57).
Research projects, especially major ones, are to short math contests NOT as a sprint to a marathon, but as Lewis and Clark’s Expedition (1804-1806) was to a sprint or a marathon. Not only longer but without a map, with many surprises and unexpected developments along the way, requiring many hard to define skills that a champion sprinter or marathon runner generally lacks.
Valuable time spent drilling and practicing known skills and studying known knowledge may detract from the time needed to explore new ideas and new methods. Some daydreaming and “laziness” may be needed, especially for radically new ideas.
I rated Peak four out of five, primarily because of the vague, shifting definition of deliberate practice in both the book and Ericsson’s scholarly work. The book is good and well worth reading. The book will give many readers insights and good ideas for practicing to improve their skills in math or many other fields. However, the complete theory of deliberate practice seems like a sweeping generalization from studies of a few highly specialized fields such as chess and violin to expertise and peak performance in many quite different fields such as mathematics, particularly applied and basic research mathematics.
The picture of science writer Malcolm Gladwell is from Wikimedia and is licensed under the Creative Commons 2.0 license. The original author of the image is Kris Krug.
© 2017 John F. McGowan
About the Author
John F. McGowan, Ph.D. solves problems using mathematics and mathematical software, including developing gesture recognition for touch devices, video compression and speech recognition technologies. He has extensive experience developing software in C, C++, MATLAB, Python, Visual Basic and many other programming languages. He has been a Visiting Scholar at HP Labs developing computer vision algorithms and software for mobile devices. He has worked as a contractor at NASA Ames Research Center involved in the research and development of image and video processing algorithms and technology. He has published articles on the origin and evolution of life, the exploration of Mars (anticipating the discovery of methane on Mars), and cheap access to space. He has a Ph.D. in physics from the University of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Technology (Caltech). He can be reached at email@example.com.
Get more stuff like this
Get interesting math updates directly in your inbox.
Thank you for subscribing. Please check your email to confirm your subscription.
Something went wrong.