It’s a cosmic joke that the very experiences we most of us try so hard to avoid—the accidents that lead us astray—are at the root of so many of our great leaps forward in science, business and the arts. These surprises that intervene in our life, be they once-in-a-lifetime eureka moments or everyday insights, provoke us to think differently about our problems. They pull us out of our comfort zones, open us to unusual ideas, and are often the pre-requisite to progress.

As strange as it may sound, we can take steps to cultivate these fortunate accidents that are so important to us. First, we must learn to recognize the five categories of unexpected events so we can allow room for them in our well-planned lives: frames, interventions, ruminations, experiments, and shocks.

• Frames. Breakthroughs often occur only after we start seeing things from a new perspective, or what we think of as reframing. They pull us away from our assumptions and into an abstract thinking mode where unexpected connections are made. We can think of the 18th century French entomologist, René de Réaumur, who observed a nest of wasps that chewing on wood, then spit it out as mush to form nests. This unexpected fact became a new frame for him to consider the rag paper shortage occurring in Europe at the time. He realized that the insects had devised a way to make paper from wood pulp—the method the modern world utilizes to this day.
  
  This specific approach to reframing—using ideas from biological systems to develop engineering solutions—has been formalized as a study known as biomemetics.
  
  
• Interventions. There are times when we are jarred into clarity by unrelated people or events. We may be moved by a child’s suggestion, an external disturbance, behaviors shaped by scarcity, or the interruption of work. For instance, the young Samuel Colt was obsessed with building a “self-reloading gun” but was unable to conceive a workable technical solution. It was an interruption that allowed him a crucial insight: his father sent him away on a trans-oceanic voyage to learn the seaman’s trade. On board the ship he noticed that the spokes on the ship’s wheel always fell in line with a clutch, no matter which way it was spun. It struck him that he could build a revolving chamber, each containing a bullet, that worked just like the ship’s wheel. The idea for the revolver was born.
  
  
• Ruminations. Undirected play, jokes and dreams represent a set of sources that have a surprisingly large potential to jog serendipity into effect. Steve Jobs dropped out of college to follow his muse, and ended up taking calligraphy lessons purely for fun. This whimsical pursuit directly led to the appearance of multiple fonts on the original Macintosh computer, and the rise of the desktop publishing industry.
  
  Dreams as well are a well-documented source of unexpected discovery. The legendary pro golfer Jack Nicklaus conceived a new golf grip in his sleep that propelled him out of a slump into a winning period. “Wednesday night I had a dream and it was about my golf swing. I was hitting them pretty good in the dream and all at once I realized I wasn't holding the club the way I've actually been holding it lately...When I came to the course yesterday morning I tried it the way I did in my dream and it worked.”
  
  
• Experiments. Side effects and by-products of directed experiments consistently lead to some of the greatest innovations. So much so, that some scientists, like Salvador Luria, have argued for a “controlled sloppiness” in experiments, “which states that it often pays to do somewhat untidy experiments, provided one is aware of the element of untidiness.”
  
  Some of the greatest business success stories are the result of such accidents. Dr. S. Donald Stookey invented the first glass-ceramic when he accidentally heated a piece of FotoForm glass to 900c rather than 600c. He was surprised when the glass didn’t melt, and even more flabbergasted when he dropped a piece of the white glass on the ground and it didn’t break. The result was a new product, CorningWare, one of the most popular kitchen items in the world for over fifty years.
  
  
• Shocks. These are the surprising external events that cause us to see things in a new light. We can be impacted by a single observation, or it may take a repeating pattern that emerges over time.
  
  For instance, when 29-year old American Howard Schultz was sent to Milan on a business trip he had a very clear goal—to buy wholesale beans for the coffee bean shop he worked for. What he found there shocked him: espresso bars on every corner that not only served fantastic drinks, but also acted as social gathering places for the gregarious Italians. It was something he had never seen before, and he suddenly knew in his bones that this concept could be huge in America. When he pitched his bosses on the idea, they replied that they had no interest in becoming a “restaurant” business. Instead he pursued the idea on his own, ultimately creating the global phenomenon known as Starbucks.

These five kinds of accidents remind us that many of the ideas and events behind our creative leaps are out of our control. Even though we can’t predict them (in fact, they often stymie our predictions!), we can train our eyes to see these patterns whenever they occur.