Head in the Cloud

It’s time to take a deep breath and stand back. What have we learned about the practical value of knowledge? A connection between income and financial literacy, which my surveys did show, is understandable. But some of the other results I’ve shared may seem arbitrary and puzzling. I found strong correlations between income and performance on quizzes of general knowledge. There were also correlations between income and specialized areas of knowledge, among them sports and pronunciation. Several topics I mentioned in the first part of the book were also predictors of income: the map test, the UK citizenship exam, and being able to name elected representatives. But results on science, celebrities, and spelling were ambiguous. I found no indication at all of a connection between income and knowledge of grammar, slang, sex, or religion.

We are used to thinking of an informal hierarchy of knowledge, one in which rote memorization of maps or sports trivia would presumably rank near the bottom. We are told that knowledge of history and literature is the mark of a good education and, usually, a good job; that science, technology, and maths majors make good money. In many ways our society rewards specialists, not generalists.

And yet, although almost all tested areas of knowledge did correlate with years of formal education, the most provocative finding is that general factual knowledge has an effect above and beyond educational level in predicting income.

There are a number of ways of accounting for that. One is that survey performance reflects the quality of education. There is a difference between having a degree from Oxbridge and the same degree from a less distinguished university. We know that graduates of prestigious universities tend to make more money. If they also know more, that could explain a correlation between knowledge and income, even when the years of education are the same. Note that the higher income enjoyed by a graduate of a prestigious university might be attributable to that school’s cachet in the marketplace, the social connections the student made in university, or having a family with the money and connections to facilitate admission to Oxbridge in the first place. Knowing more facts than graduates of less prestigious schools might have little to do with it.

An alternative possibility is that the correlation reflects the quality of the student. Some students buckle down and learn; others coast. The survey results could reflect how engaged the participants were with learning, in school and beyond. If that’s the case the results certainly suggest that it pays to be engaged and to retain what you learn.

Lifelong attitudes to learning are likely an important factor. In effect, one question the data-crunching posed was: What do high-income people know that low-income people of the same educational level don’t know? The answer might be: Material not in the curriculum. Personal finance and sports trivia are not emphasized in school. Nor does schooling help an adult long out of school name her current elected representatives or locate nations that have only recently come into existence.

The map test is as much about current events as schoolbook geography. Essentially everyone can find Spain, Russia, and Australia. The variance in survey scores comes mainly from new nations and obscure ones not emphasized in geography classes. There are maps in newscasts, infographics, history books, apps, and airline ads. The map test is a measure of paying attention—and, as the poet John Ciardi put it, “We are what we do with our attention.”

Paying attention may be a good two-word description of what is driving the income correlation. It is most reliably measured by an assortment of general-knowledge questions that are neither too difficult nor too easy. Someone who scores low in general knowledge is probably not paying much attention to the outside world, whereas someone who scores high has been absorbing a lot, resulting in broad (if superficial) contextual knowledge.

A set of spelling questions, say, is likely to be less informative. Knowing how to spell “prerogative” correlates strongly with knowing how to spell “consensus” or “supersede.” It’s basically the same group who knows how to spell frequently misspelled words. Yet of course there are many brilliant people who can’t spell, and some have quite encyclopedic knowledge otherwise. For that reason, a focused set of questions—on spelling or any other narrow topic—is less likely to achieve statistical significance as a predictor of income.

Easy questions seem to be better predictors than hard ones. Here’s a scatter chart showing performance on quizzes of general and specific knowledge. Each black dot represents a survey. The horizontal axis shows how difficult the survey was, measured by the average percentage of questions answered correctly. The vertical axis shows the income advantage of the highest scorers over the lowest scorers. As usual, we’re looking at the projected income difference between a thirty-five-year-old with four years of university who got all the questions right versus a thirty-five-year-old with four years of university who missed all the questions.

For instance, a map test that included rather easily identifiable nations such as Russia, Japan, and Turkey had an average score of seventy-six percent (dot at upper right). Performance on this quiz was a good predictor of income, with high scorers reporting about $71,000 (£47,000) more household income per year than low scorers.

In the lower part of the chart, at left centre, is a set of ten fairly difficult questions taken from a TV quiz show (Jeopardy!). These questions were harder—the average score was only forty-three percent correct—and the income difference was less: $13,000 (£8,500) a year.

The connection between difficulty and income difference is certainly noisy, but the cloud of dots generally runs from lower left to upper right, implying that the easier the question, the stronger the connection to income.

To test this idea, I sent out some linked surveys. Everyone in a randomized group answered a set of “easy” questions and a set of “hard” questions on an identical assortment of topics. This method eliminates most of the variables, as distribution of income, education, and other demographics remained constant within the sample. The only variable was the difficulty of the questions.

The chart’s dashed lines join surveys sharing the same set of participants. Both lines slope upwards. For each of the two randomized groups, the easier set of questions was associated with a greater income difference than the harder set. (The difficult survey at bottom centre is shown as a hollow dot, as it was not statistically significant. Both of the easy surveys, and the other hard survey, were highly significant.)

On a quiz show, answering difficult trivia questions is worth more money than answering easy trivia questions. Real life seems to be different. There’s a real advantage to knowing what the crowd knows, but there are diminishing returns beyond that.

Another way of thinking about it is that there is an income penalty for not knowing widely known facts. A graduate who cannot identify Sputnik or Ernest Hemingway (two of the “easy” questions on the general-knowledge surveys) has not got much out of her education and lacks the level of cultural literacy that most of her fellow graduates have.

But there is not much of a prize for knowing little-known facts unrelated to one’s work. I am not challenging the value of being an expert in something. Every professional has to be. But that’s not what my surveys were intended to gauge or were able to gauge. They point instead to the value of a liberal education in the broadest sense of the term—and, above all, to the value of paying attention.

The connection between knowledge and income raises questions about what causes what. Is it possible that knowledge enhances mental ability? This question has been studied in connection with the game of chess.

For several years the famed director Stanley Kubrick worked as a chess hustler in New York City parks. He spent up to twelve hours a day playing chess, earning about $20 a week. As Kubrick later explained,

chess is an analogy. It is a series of steps that you take one at a time and it’s balancing resources against the problem, which in chess is time and in movies is time and money.… You sit at the board and suddenly your heart leaps. Your hand trembles to pick up the piece and move it. But what chess teaches you is that you must sit there calmly and think about whether it’s really a good idea and whether there are other, better ideas.

Chess figures in several of Kubrick’s films. The chess game in 2001: A Space Odyssey, between an astronaut and the homicidal computer HAL, is adapted from the 1910 match between Otto Roesch and Willi Schlag in Hamburg. The astronaut resigns, leaving HAL to retort, “Thank you for a very enjoyable game.”

Chess plays an important role in the history of artificial intelligence. Since the dawn of the computer age, it has been used as a model of human expertise. Chess is a difficult game with simple rules. The rules are easily coded; the expertise is not. Knowing the rules does not make a human (much less an algorithm) a good chess player. Nor does knowing the history of chess and chess trivia or memorizing a few famous matches. What does a good chess player know that a poor one doesn’t? Is chess ability an innate talent one is born with, or is it a skill that can be acquired through long practice? These questions have engaged chess players since the game began, and psychologists and computer scientists as well.

Dutch chess master Adriaan de Groot, who represented the Netherlands in the Chess Olympiads, was also a psychologist. He asked expert and novice chess players to document their thought processes and was surprised to find that there weren’t many overt differences. You might think that the master players would have looked ahead by more moves or have evaluated more potential moves than the beginners did. They didn’t. Instead the expert players had better instincts. They spent more time analysing promising moves and less time analysing lousy moves. The beginners did the opposite. The mind of a great chess player has more efficient code, not a faster processor.

De Groot is best known for a remarkable experiment. He showed players chessboards set with configurations of pieces from actual games for five seconds. After that brief viewing, the players were asked to reproduce the boards’ configurations from memory.

The master players were incredibly good at this. They reproduced the exact positions of every single piece with virtually 100 percent accuracy. Lesser players were hopeless, often with accuracies of 20 percent or less.

De Groot then conducted a telling variation on the experiment. He showed players chessboards set at random—arbitrary configurations of pieces that had not and probably could not have arisen in play. This time the masters were no better than the novices. All struggled to remember the location of even half a dozen pieces.

Good players are better at remembering realistic board configurations only. They do this by recognizing patterns they’ve seen before—gambits and sacrifices and strategies. Artificial intelligence pioneer Herbert A. Simon, who repeated de Groot’s experiments, maintained that good players categorize the board’s configuration into “chunks,” facilitating memory.

This strategy is not limited to chess. A novice birdwatcher sees only a blur of colour and feathers. He is unable to categorize the bird he sees; he does not know which features are diagnostic and which are irrelevant. The novice struggles to remember everything about the bird—an impossible task—in order to consult a field guide. An expert immediately recognizes an immature female golden oriole and need only remember that categorization. In broad outline this analysis applies to anything we do with deliberation and imagination—running a business or a marathon; designing an app or a wedding; understanding a frightened child or a TED talk. By recognizing familiar patterns we make sense of a complex whole.

No one is saying that the ability to remember a chess position is the only distinction of a master player—or even the most important distinction. That ability is necessary but not sufficient. As Kubrick had it, chess is a game of opportunity costs. It is not enough to conclude that a move is a good one. The master player must always be asking, is there a better move? Critical thinking is paramount, but memory lays the groundwork: a player who must constantly keep looking back at the board just to recall where the pieces are now will be severely handicapped in that weighing of options.

It is natural to ask whether the ability to categorize/memorize a chessboard, acquired from long practice, constitutes knowledge, skill, or talent. Maybe the best answer is that the question is wrong. Knowledge, skill, and talent are labels we have made up to describe mental processes that we don’t deeply understand. They may not have much to do with the cognitive ground truth.

Chess is popularly caricatured as the epitome of logic and thus the proper domain of Deep Thought, HAL, and other soulless entities. But as the game is played by humans, it is no less an exercise in intuition and the unconscious. Good players acquire the ability to recognize chessboard configurations that occur during play. Logic has nothing to do with this: it’s more like recognizing a familiar face in a crowd. No one is born knowing the inner game of chess. Chess masters acquire their intuitions by learning many “facts” and also by knowing how those facts fit together globally. Learning facts is one way we build intuitions, and these are the fundamentals of so-called skills and talents.

In the early 1950s, Bette Nesmith Graham was a divorced single mother who took a job as a secretary at Texas Bank and Trust. The bank had just outfitted its offices with IBM Selectric typewriters. They came with one big drawback. The Selectrics used a carbon film ribbon that produced crisp type that was impossible to erase. A single error meant that an entire page had to be retyped.

Bosses, who were men, didn’t care. Women’s labour was cheap, so much so that Graham supplemented her meagre income by painting Christmas decorations for the bank’s windows. The exercise reminded her of something she’d once learned: artists painted over their mistakes rather than erasing them.

And that’s what led Graham to her eureka moment. She realized she could paint over typing errors rather than erase them. She mixed white tempera paint in her kitchen blender and put it in a little bottle. Whenever she made a typo, she blotted it out with a brush, waited a few seconds for it to dry, and typed over it. Marketed as Liquid Paper, the invention became one of the bestselling office supplies of the late analogue age. In 1979 Graham sold her company to Gillette for $47.5 million.

“Imagination is more important than knowledge,” Albert Einstein wrote in 1931. But it’s also true that the latter undergirds the former. What we call imagination often involves making a connection between two facts—seeing the relevance of a painter’s solution to a typist’s problem, say. Einstein was interested in a branch of mathematics with no practical value—the non-Euclidean geometry of Bernhard Riemann. Physicists did not study Riemann because his work had no connection to physics. Einstein’s greatest eureka moment was realizing that Riemann’s geometry could be the basis of a new theory of gravity, one in which matter warps space and time.

In cases like this, knowledge and imagination go hand in hand. There was a generation of physicists working on a new theory of gravity and a tiny group of mathematicians who knew of Riemann’s work. Einstein, and perhaps no one else, fell in the intersection of that Venn diagram.

There are many other examples of this phenomenon. Charles Darwin and Alfred Russel Wallace were both interested in the origin of species. Each had read a topical book on the origin of poverty, Thomas Malthus’s An Essay on the Principle of Population. They both made the same connection and came up with similar theories of natural selection.

Aaron Copland knew American folk music along with Schoenberg’s twelve-tone system. Picasso was among the first classically trained European artists to study African sculpture. Mark Zuckerberg knew how to code and also how much Harvard students used their printed student directory, the “face book.”

We all confront problems in our lives and careers. In ways big and small, “irrelevant” knowledge can be a source of analogies, inspirations, and solutions.

Learning changes not just habits of thought but also brain anatomy. It’s conjectured that London black taxi drivers learn more discrete facts than do practitioners of any other profession. This has recommended the profession to neuroscientists. They report that the posterior hippocampus, the brain’s primary site for creating new long-term memories, enlarges during the process of studying for the drivers’ Knowledge exam and remains larger than those of the public.

A 2015 report in Nature Neuroscience found that children of well-educated and well-to-do parents had a greater cortical area than children of less educated and less affluent parents. The cortical differences were particularly notable in regions of the brain connected to language, reading, and decision-making. The study didn’t directly address the reasons, but explanations weren’t hard to find. “Money can buy better education, homes in areas further away from freeways,” said lead researcher Elizabeth Sowell. “It can buy guitar lessons. It can buy after-school programmes.” The act of learning the guitar can lead to more capable brains and other advantages, even for those who do not intend to become professional guitar players.

One possible explanation for the connection between broad factual knowledge and income is that learning improves cognitive abilities that are useful in almost any task, including a career. Learning causes better brain function, which in turn causes higher income.

No one would claim that ride-sharing apps and Segways have made walking obsolete. Exercise is needed for the human body to function; whether it is also needed to get from point A to point B is beside the point. Our brains need the process of learning to function at peak performance. That facts can be looked up elsewhere doesn’t change that.