Henri Poincaré put his foot on the step of an omnibus at Coutances, in Normandy, in 1880, and the idea came at that instant. It told him that the transformations he had used to define a new family of functions, the ones he would name Fuchsian, matched those of non-Euclidean geometry. He took his seat, went on with a conversation already under way, and rode off to what he later called "some place or other." He checked nothing. "I felt a perfect certainty," he told a Paris audience in 1908.

The certainty had a history. For fifteen days before the trip, Poincaré had spent an hour or two a day at his work table in Caen on combinations meant to prove that no such functions could exist, and none of them worked. One evening, against his habit, he drank black coffee and lay awake while ideas "rose in crowds," and by morning he had built one class of the very functions he had set out to rule out. Then a geological excursion run by the School of Mines took him out of Caen, and the travel pushed the mathematics out of his head.

Poincaré read the sequence as "a manifest sign of long, unconscious prior work." Eighteen years after that Paris talk, an English social psychologist gave each part of that work a name.

The Why

In The Art of Thought (1926), Graham Wallas of the London School of Economics set Poincaré's account beside one from the German physicist Hermann von Helmholtz. At a banquet for his seventieth birthday in 1891, Helmholtz said his happy ideas never came "when my mind was fatigued, or when I was at my working table." They came after he had investigated a problem "in all directions," and most readily "during the slow ascent of wooded hills on a sunny day." Wallas found three stages in Helmholtz's account and wrote, "And I shall add a fourth stage, of Verification." Together they make The Four Stages of Creativity.

Preparation is the conscious, head-on work, the hours Poincaré spent failing at his table.

Incubation begins when the maker turns to something else and the problem stays open out of sight.

Illumination is the answer surfacing, often whole, on a hillside or an omnibus step.

Verification sends the maker back to the desk to test the answer.

In 2009 the psychologists Ut Na Sio and Thomas Ormerod pooled 117 studies of incubation with 3,606 participants and found that a break improved the odds of a solution. A longer stretch of preparation made the break pay more, and demanding work during the break made it pay less.

The flash keeps its own hours. The other three stages go on a calendar, and they set what the flash has to work with.

The How

Poincaré ran The Four Stages of Creativity by accident, with a geology trip for a break. A working creative can run them on purpose.

  1. Define the specific problem. Poincaré spent fifteen days on one question with a yes-or-no answer, whether functions of this kind could exist at all. The pharmacologist Otto Loewi had voiced one hypothesis seventeen years earlier, that nerves signal by chemistry, and the idea that woke him one night was an experiment to test it. Write tomorrow's problem as one question narrow enough to answer with a scene or a chord change. "How does the letter reach her before the wedding?" gives the night something to work on, and "fix act two" leaves it idle.Saturate yourself completely. Spend focused time with the problem. Try solutions. Read everything relevant. Sketch, prototype, write terrible first drafts. You’re not wasting time when you fail here. You’re programming your unconscious with variables and constraints. Load the gun before you expect it to fire.
  2. Saturate yourself completely. Poincaré wrote that his inspirations "never happen except after some days of voluntary effort which has appeared absolutely fruitless," and Sio and Ormerod's finding on longer preparation backs him. Book a fixed daily block for the problem and keep a failure log with one line per dead end: the chord progression that stalled, the ending that went soft. Stop when new attempts start repeating old ones.
  3. Walk away strategically. Helmholtz climbed wooded hills. In Sio and Ormerod's data, a demanding task during the break shrank the effect, and on word puzzles an easy task beat plain rest. Choose the break before you stop, a walk on a familiar route or a sink full of dishes. Keep other hard work out of that hour, and count sleep as a break too.
  4. Capture the flash. Keith Richards kept a Philips cassette recorder by his bed. One morning in 1965 he woke to find the tape run to the end and played it back: about two minutes of acoustic guitar, the pick dropping, then forty minutes of snoring. "I actually dreamt the damned thing," he told NPR in 2010. On May 10, 1965, the Rolling Stones recorded the riff at Chess Studios in Chicago as "(I Can't Get No) Satisfaction." Put a recorder or notebook beside the bed and in the bathroom, and set the phone's voice memo to open with one press.
  5. Test without mercy. Poincaré's certainty survived the desk in Caen, and he still warned that the feeling "often ... deceives us without being any the less vivid." Doubt needs the same test. Richards heard his fuzz riff as a stand-in for horns and told the band the song could not come out as a single. Brian Jones, Charlie Watts, Bill Wyman, and their manager, Andrew Loog Oldham, outvoted him, and the record reached No. 1 in the United States on July 10, 1965. Within two days of a flash, build its smallest finished version, the scene written out or the riff recorded, and show it to one person who has not heard how it arrived.

Pro-tip: Log two dates for every problem, the day you stopped working it and the day the answer came. After a few problems, the gaps show roughly how far ahead of a deadline to stop preparing.

Mistakes to Avoid

  • Skipping preparation. Ullrich Wagner's 2004 study of sleep and insight named its own limit: "Sleep did not enhance insight in the absence of initial training." A songwriter who naps on a chorus she never tried to write wakes up rested and still without a chorus.
  • Grinding through exhaustion. Helmholtz's ideas never came when he was tired or at his working table. The designer re-kerning one logo at two in the morning, for the fifth night, is sitting at that table.
  • Forcing illumination. Wallas held that the flash cannot be influenced "by a direct effort of will." A screenwriter who stares at the blank scene and orders the ending to arrive keeps the problem in preparation. Take the break from step 3 and leave the notebook open.
  • Trusting the flash blindly. In an 1870 talk at Harvard, the physician and writer Oliver Wendell Holmes Sr. described breathing ether and grasping "the one great truth which underlies all human experience." As the ether wore off, he staggered to his desk and wrote it down. The page read: "A strong smell of turpentine prevails throughout." A flash arrives with its certainty attached, and only the page can check it.
  • Scrawling notes you cannot read. On the night before Easter Sunday, Loewi woke with his idea, turned on the light, and wrote "a few notes on a tiny slip of thin paper." At six in the morning he could not read his scrawl. The idea returned the next night at three, and he went straight to the laboratory for the frog-heart experiment that won him a share of the 1936 Nobel Prize. Read a half-asleep note aloud into the recorder before lying back down.
  • Using incubation as an excuse. A break counts as incubation only when failed work sits in front of it. The novelist who has not opened her manuscript in three months and calls it incubating has an empty failure log. With less than a week of attempts in the log, the problem needs preparation, and the break is a holiday.

What the Sleeping Brain Does With a Problem

Wagner's volunteers reduced strings of digits by two simple rules, and the strings hid a shortcut. After eight hours of sleep, 59 percent found it, against 23 percent after eight hours awake.

Salvador Dalí worked the edge of sleep on purpose. In 50 Secrets of Magic Craftsmanship (1948), he told painters to doze in "a bony armchair, preferably of Spanish style," with a heavy key pinched between thumb and forefinger over a plate turned upside down on the floor. When sleep loosened the fingers, the key fell, and the clatter woke the sleeper.

In 2021 a team at the Paris Brain Institute gave 103 volunteers the same kind of digit task and a light bottle to hold. Those who spent at least fifteen seconds in the lightest stage of sleep found the shortcut 83 percent of the time, against 31 percent for those who stayed awake and 14 percent for those who slid into deeper sleep. Dalí's key marked a window a few breaths wide.

Reading a Block by Its Stage

The omnibus step was the first of three sudden flashes in Poincaré's account. After more failed work, he spent a few days at the seaside, "disgusted with my failure," and on a bluff one morning the next idea came with the same "brevity, suddenness and immediate certainty." A third came as he walked along a street, and between flashes he went back to the desk. Wallas allowed for it: "In the daily stream of thought these four different stages constantly overlap each other as we explore different problems." He also named the moment just before a flash intimation, when an association is rising at the fringe of awareness.

Poincaré had a theory of why the right idea surfaces. The unconscious, he proposed, throws up great numbers of combinations, "almost all ... without interest and without utility," and taste picks the few that reach awareness, because "the useful combinations are precisely the most beautiful." He called that sense "the delicate sieve." If he was right, the hours at the table load the problem and train the sieve at once.

Read through The Four Stages of Creativity, a block is a stage mismatch, and each symptom points to its stage:

  • The block comes after two hours of work. Preparation has barely started, and a break would have too little to work on. Go back to the table.
  • The block comes after two weeks of grinding. Incubation never began. Stop, pick an easy break, and move a different problem into preparation while this one sits.
  • The answer on the page looks wrong. Intimation may have passed for the answer, or the flash misfired. Write down what looks wrong and carry it back into preparation as a new constraint.
  • The idea breaks on contact. Verification is working. Poincaré's idea survived Caen, and Holmes's great truth did not survive his own handwriting. Log what broke and return to step 2.

The omnibus pulled out of Coutances with Poincaré still talking, bound for some place or other, and his account leaves the talk blank. Back in Caen he verified the idea from the step "for conscience' sake," and the result stood. The Four Stages of Creativity put the table, the break, and the test on a creative's calendar, and they leave the flash to its own hours. Poincaré's work table had held the problem for fifteen days before the trip. The step held his foot for a second, and then it held the next passenger's.