The two speeds of thought

Try this before reading on. A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?

A number leaps to mind: 10 cents. It is wrong. If the ball cost 10 cents, the bat would cost $1.10 and the pair $1.20. Call the ball's price x: then x + (x + 1.00) = 1.10, so the ball is 5 cents and the bat $1.05. The puzzle is not hard, and a few seconds of checking would catch the slip. It is a trap because System 1 hands over an answer first, and that answer feels so obviously right that System 2 never checks it.

Kahneman drew the lesson plainly. Anyone who says 10 cents did not check. Their System 2 accepted an intuitive answer that it could have rejected with a small effort.

In 2005 the decision researcher Shane Frederick made the bat-and-ball puzzle one of three items in a Cognitive Reflection Test. Each item has an answer that springs to mind and is wrong. Another asks how long 100 machines take to make 100 widgets, if 5 machines take 5 minutes to make 5. The tempting answer is 100 minutes; the right one is 5.

Frederick gave the test to 3,428 people, mostly university students. Only 17 per cent got all three right, and a third got none. The test also showed how the mistake feels from inside. People who answered 10 cents guessed that 92 per cent of others would solve the puzzle. Those who answered 5 cents guessed 62 per cent. They had noticed the trap, so they knew it could catch people. The ones it caught thought the puzzle too easy to miss.

Why does System 2 let such errors through? In Kahneman's account it can monitor System 1's suggestions and overrule them, but it is reluctant to spend more effort than it must. He calls it a lazy controller.

Logic shows the same pattern. Decide quickly whether this argument holds: all roses are flowers; some flowers fade quickly; therefore some roses fade quickly. A large majority of college students accept it. It is invalid, because the flowers that fade quickly might include no roses at all. The conclusion sounds true, and that feeling does the work that checking the logic should have done. When a conclusion already seems believable, people readily accept an argument for it, even a broken one. The conclusion comes first, and the reasons follow.

The effort of System 2 is not only a feeling; it shows in the body. In the 1960s Kahneman and his student Jackson Beatty filmed people's eyes while they did tasks paced by a metronome. In one, called Add-1, you hear four digits and must say each one plus 1, so 5294 becomes 6305. Add-3 adds 3 to each digit and is much harder.

The pupil, the dark opening at the centre of the eye, turned out to be a faithful gauge of the effort. It widened with every digit held in mind, peaked as the answer was produced, and shrank back as the load was let go. In the first five seconds of Add-3 its area grew by about 50 per cent, and heart rate rose by about seven beats a minute. Ordinary conversation barely moved it.

Effort draws on attention, and attention is limited. Kahneman and Beatty showed what happens when it runs short. While people did Add-1, letters flashed quickly on a screen in front of them, and afterwards they were asked whether a K had appeared. They almost never missed a K shown near the start or the end of the task. At the peak of effort they missed it almost half the time, although their wide-open eyes were looking straight at it.

This is the limited capacity of System 2. When demand is too high, it does not shut down everything at once, the way a fuse cuts a whole circuit. It protects the most important task and lets the others go unseen. That is why a driver stops talking while turning across heavy traffic.

Some questions are hard to answer properly. How happy are you with your life these days? calls for a review of work, health, family and more. System 1 has a shortcut. It quietly answers an easier, related question instead, such as what is my mood right now? Kahneman and Shane Frederick called this swap substitution.

A 1988 survey of German students by Fritz Strack and his colleagues shows it at work. When students were asked how happy they were and then how many dates they had had last month, the two answers were barely related. When the dating question came first, the link jumped to a correlation of 0.66, very high by the standards of psychology. Thinking about their love lives had left a feeling behind, and that feeling answered the bigger question. Nobody noticed the swap.

System 1 is also swayed by numbers that should not matter. The best-known case is anchoring: an estimate stays close to a number you have just considered, even a number you know to be random.

In a 2006 study, Birte Englich, Thomas Mussweiler and Fritz Strack gave young German judges the case of a woman caught shoplifting for the twelfth time. Each judge rolled a pair of dice, loaded to total 3 or 9, and was told to treat the roll as the prosecutor's demand in months. Judges who rolled a 9 went on to give her about 8 months on probation; those who rolled a 3 gave her about 5. In a companion study, judges with thirteen years in court on average were swayed too, by a demand they were told was random.

System 1 builds the best story it can from whatever information is in front of it, and does not ask what is missing. Kahneman gave this habit a clumsy abbreviation, WYSIATI, for what you see is all there is.

A 1996 study by Lyle Brenner, Derek Koehler and Amos Tversky shows the cost. People read the facts of a legal dispute. Some then heard both lawyers argue; others heard only one side, and knew it. The one-sided arguments swayed their judgments strongly, and people who heard only one side were more confident than those who heard both. That is what you would expect if confidence comes from how coherent the story is, not from how complete the evidence is. Knowing little can even make it easier to build a coherent story.

System 1 keeps track of how smoothly things are going. A clear font, a familiar phrase, a claim you have met before: each is taken in easily, and that smoothness creates a feeling Kahneman calls cognitive ease. The trouble is that ease also feels like truth.

In a 1977 study, Lynn Hasher and her colleagues showed students 60 plausible statements, some true and some false, in three sessions two weeks apart, and asked how true each one was. Twenty statements appeared in every session. Those repeated statements were rated more true each time, while ratings of new statements stayed flat. The effect has been found again many times since. Repetition makes a claim familiar, familiarity makes it easy to take in, and System 1 reads that ease as a sign that the claim is right.

Not all intuition is guesswork. The psychologist Gary Klein studied firefighting commanders, and tells of one who led his crew into a house with a kitchen fire. As they sprayed water, he heard himself shout to get out, without knowing why. Moments after they left, the floor collapsed. The heart of the fire had been in the basement beneath them. Only later did he realise what had warned him: the fire was unusually quiet, and his ears were unusually hot.

Herbert Simon, who studied chess masters, explained such feats plainly. The situation provides a cue, the cue gives the expert access to information stored in memory, and that information provides the answer. Intuition, he wrote, is nothing more and nothing less than recognition. An expert's sudden knowing works like spotting a friend's face in a crowd.

So when can an expert's intuition be trusted? Kahneman had spent a career on errors of judgment, and Klein one on expert skill. In 2009 they published a joint answer.

The feeling of confidence is no guide, they agreed, because confidence comes from how easy the story is to tell, whether it is right or wrong. Look instead at how the intuition was learned. Skilled intuition needs two things. The first is a regular environment, one whose cues really do predict what happens next, as in chess, firefighting or nursing. The second is long practice with feedback that is fast and clear, so the person learns which cues matter. Where the world is not regular enough, as for stock pickers or pundits making long-range political forecasts, years of experience produce confidence without skill.

How literally should all this be taken? Kahneman himself called System 1 and System 2 fictitious characters. They are not places in the brain, he wrote; no one part of the brain would call either of them home. They are a way of talking, because a sentence about what an agent does is easier to follow and remember than a list of mental properties.

Some findings in the book have also fared badly. Studies of behavioural priming, in which a passing idea supposedly nudged later actions, often gave weak or no results when other labs repeated them, and in 2017 Kahneman wrote that he had placed too much faith in small studies. In 2016, a test across 23 labs of ego depletion, the idea that self-control runs down with use, found almost no effect. The bat-and-ball puzzle and the basic anchoring effect, by contrast, still hold up.

Muslim scholars also asked what careful thinking is. In the book on reflection in his Iḥyāʾ ʿulūm al-dīn, al-Ghazālī, who died in 1111, defined it: to reflect is to bring two pieces of knowledge together in the heart so as to draw a third from them.

His example is a person drawn to the pleasures of this world. He can accept that the hereafter deserves to be preferred simply because someone told him so. That, al-Ghazālī says, is imitation (taqlīd), not knowledge. Or he can know that what lasts deserves to be preferred, and know that the hereafter lasts; from these two he draws a third, that the hereafter deserves preference. Reflection is the patient work of joining what you know. In a hadith in Ṣaḥīḥ Muslim, the Prophet told al-Ashajj of ʿAbd al-Qays that he had two qualities Allah loves: forbearance and unhurried deliberation.