Any time, at any age

Retired at seventy

In June 1987 the chemist John Fenn turned 70. Yale University, where he had taught for twenty years, had a rule that professors retire at that age, and Fenn became a professor emeritus with a smaller laboratory and fewer resources. He had spent his career on gas jets and molecular beams and had published his first research paper at 32. Most people would have said his big years were behind him. Instead he kept working on a problem that had begun to interest him a few years earlier: how to turn large molecules, such as proteins, into charged gas-phase ions so that a mass spectrometer could weigh them, without breaking them to pieces. In October 1989, aged 72, he and his colleagues published a paper on the method, called electrospray ionization, that opened the door to weighing the molecules of life. In 2002, at 85, he shared the Nobel Prize in Chemistry for it.

Fenn is a good place to begin the third question of this course. We have asked how success relates to performance, and how large it can grow. The next question is when it arrives in a career. The source lectures make a bold claim, the sixth of their ten rules: success can come at any time. A person’s best work is as likely to come late as early; what changes with age is not the chance of each try but how many tries are made. This lesson looks at the evidence, and at a model that goes with it, the Q-factor.

The young genius

The opposite view is ancient and respectable. Scientists, poets, and mathematicians have long said that creativity belongs to the young. The physicist Paul Dirac is said to have written a little verse to the effect that a physicist past thirty had better be dead. A remark often attributed to Albert Einstein says that anyone who has not made a great contribution to science by the age of thirty never will, though no one has found where, or whether, he said it. (His own general theory of relativity was completed when he was 36.) The pioneers of quantum mechanics seemed to prove the point: Werner Heisenberg’s matrix mechanics came at 23, Dirac’s equation for the electron at 25.

But the pioneers are a tiny, famous group, and the picture changes when you count everyone. Enrico Fermi’s theory of beta decay came at 32 or 33, past the supposed deadline. The economist Benjamin Jones found that only about 7 percent of Nobel-winning work was done at 26 or younger, and that among Nobel laureates and great inventors together the average age at the time of the work rose by about six years over the twentieth century, as training got longer and fields grew larger. Famous young geniuses are remembered; the late breakthroughs are not told as often, because they make a worse story.

What about business? The lectures say that the founders of billion-dollar companies come in a flat spread from their twenties to their seventies. We could not find a source for that exact claim, but the best data point the same way. A study by Pierre Azoulay and colleagues followed 2.7 million people who founded companies in the United States between 2007 and 2014, using tax and census records. The average age of the founders was 41.9, and for the fastest-growing one company in a thousand it was 45. A 50-year-old founder was about 1.8 times as likely as a 30-year-old to start a company that reached the top tier of growth, and the probability rose with age up to about 60. The young founders we hear about (Silicon Valley loves a 22-year-old) are the visible tail, the ones the newspapers write about.

Lottery tickets

The lectures make the point with a particular study. In 2016 Roberta Sinatra and colleagues published a study of scientific careers, using the records of the American Physical Society, which publishes the Physical Review journals. From 236,884 physicists they picked the 2,887 whose careers lasted at least 20 years, with at least 10 papers and a paper at least every five years. (That is about one percent. The authors call them survivors of many selection steps, and the findings apply to them.) Success, for each paper, was measured by its citations ten years after publication.

The question was when in a career the most-cited paper appears. For these physicists it was about equally likely to come at any point in the first twenty years or so, and rarer after that, partly because only careers lasting twenty years are in the sample. That alone looks like the old story, that discovery belongs to the young. But then the researchers did a clever test. For each physicist they kept the list of papers and the years in which they were published, and shuffled the citation counts among the papers at random. The shuffled careers gave the same curve as the real ones. The timing of the best paper was fully explained by how many papers were published in each year and by which careers were in the sample. A second test asked where the best paper sits in the sequence of a scientist’s papers: first, tenth, or last. The answer was flat. The best paper is as likely to be the first as the last, or any between.

This is the “random impact rule.” The best work is equally likely to be anywhere in a scientist’s sequence of work. Papers are written in every year of a career, but fewer careers last thirty or forty years, so there are fewer tickets late, and the best papers pile up where the papers pile up. The lectures compare it to lottery tickets: each paper is a ticket, and if most of your tickets are bought in your first twenty years, most of your prizes will be won then. The comparison is picturesque, but the shuffling test is what supports it. (In psychology the idea is older, under the name equal-odds rule; the 2016 study confirmed it on a large scale.)

Two of the study’s examples sit at the two ends. The physicist Frank Wilczek published a paper in 1973 as a 21-year-old graduate student at Princeton. It showed that the force that binds quarks gets weaker at short distances, and in 2004 it earned him a share of the Nobel Prize in Physics, 31 years later. (The lectures say “four years” later; that is not right.) John Fenn’s prize-winning paper, as we have seen, came at 72. Both fit the same rule. One tells you that the best work can come very early, and the other that it can come very late. Neither tells you that age matters.

Hot streaks

The random impact rule says that each paper’s impact is drawn independently of when it comes. It does not say that a career is a series of independent draws, and the picture was soon refined. In 2018 Lu Liu and colleagues studied three kinds of career: 3,480 artists (with the prices of their works at auction), 6,233 film directors (with audience ratings of their films), and 20,040 scientists (with the citations of their papers). They found that the best works in a career tend to cluster. The second-best work was about 1.4 to 1.6 times as likely as chance to sit next to the best one. The researchers called this a hot streak: a period, usually of about five years, when everything a person produces is better than usual. By their definition, between 82 and 91 percent of the careers contained at least one, and some contained two. When a streak begins within a career is as random as the best work was, and nothing changes in how much the person produces. Their output is the same; its quality is higher. Why it starts, and why it ends, is not known, and the authors stress that “hot streak” is a description, not a cause. A follow-up in 2021 found that before a streak, people had been exploring a wide range of styles or topics, and that afterwards they focused more narrowly. That is correlation, not proof of a recipe.

The streaks do not contradict the rule, because the start is still random. They do soften the lectures’ claim that success is “a singular event” with nothing before or after. On average the best paper looks like an isolated spike; on closer inspection careers have hits in clusters. There is also a critic: another team, studying over 100,000 scientists, found that runs of success are more common early and late in a career than in the middle, and suggested that the average length of a streak in the 2018 paper may be an artifact of how it was measured. The evidence is good enough to take seriously and unsettled enough to hold lightly.

Idea times skill

If the best work is a lottery ticket, why do some scientists win so much more often than others? The 2016 paper proposed a simple model. Each project has a potential impact, which the model calls p and treats as luck: a random number, drawn from the same pool for everyone, that depends on the idea. Each person has a factor, Q, that stands for their ability to turn an idea into something the community values. The impact of a paper is then the product of the two: impact = Q × p. A scientist with a high Q can publish a bad paper if the idea was weak, and a scientist with an ordinary Q can publish a hit if the idea was strong. But over a career, the person with the high Q is the one who gets the hits most often.

The study fitted this to the physicists’ data and reported several findings. Q follows a bell-shaped curve on a logarithmic scale, with most scientists near the middle and a few far above. It seems to stay about constant over a career for about three quarters of scientists, and it can be estimated with an error of under ten percent once a scientist has about 20 papers. It is only weakly to moderately related to how much a scientist publishes, so that high output does not make up for a low Q: a scientist with a low Q who doubles the output gains little, while one with a high Q who does so gains a lot. And Q ranks the scientists who later won Nobel Prizes higher than other measures do: the area under the curve that measures how well a ranking finds the laureates was 0.94 for Q, 0.90 for the h-index (a common count of cited papers), and 0.65 for the number of papers published. That ranking was made after the fact, from whole careers, and by one independent count it rests on only about 25 laureates, so it says that Q is a good description of such careers, not that it can forecast prizes.

The lectures illustrate the multiplication with Apple. Apple’s first handheld computer, the Newton, was a great idea poorly carried out, the Power Mac G4 Cube was a handsome machine that sold poorly, and the iPhone was a great idea well executed. (The lectures credit the Newton to Steve Jobs. It was not his: it went on sale in 1993, under the chief executive of the time, John Sculley, while Jobs was away from Apple, and Jobs ended it in 1998.) The cleaner example is the Cube and the iPhone, both the work of Jobs’s Apple and its design team. The Cube was announced in July 2000 at $1,799, and production was suspended in July 2001, with about 150,000 sold. The iPhone went on sale in June 2007 and sold its millionth unit 74 days later. It is an illustration, not a test of the model: Apple itself said that most customers chose its Power Mac G4 minitowers instead of the Cube, and ideas and execution cannot be pulled apart so neatly.