We frequently wonder where ideas come from. How did Thomas Edison and Nikola Tesla come up with a continuous stream of inventions over decades? An often repeated tale about Edison says that when facing a tough problem he would sit down in a comfortable chair with a metal ball in his hand. As he drifted off to sleep the ball would fall to earth and waking him, and the solution to the problem would be there – clear in his mind.
I don’t know whether this story is true. But many mathematicians have solved difficult problems while dreaming, or while not consciously working on them. The famous Indian mathematician Srinivasa Ramanujan claimed that his family goddess would present him with complex mathematical equations in his dreams. In another example, a mathematician included a dead friend who was not a mathematician as a co-author on a manuscript that was a culmination of years of work. He explained that the deceased friend came to him in a dream and provided a crucial insight that allowed him to complete his efforts.
The famous French mathematician Henri Poincaré was very interested in mathematical creativity. He describes a period of hard and seemingly fruitless effort to solve a problem, from which he took a break to join a geological expedition. As he was stepping on a bus, he made one of the most important breakthroughs of his life. The solution came to him out of nowhere, and was accompanied by a perfect certainty as to its correctness.
We know that at any moment we are aware of only a fraction of what goes on in our brain. Indeed, Poincaré was quite aware that creativity requires a period of conscious effort followed by a period of rest. Our unconscious mind keeps working on the problem behind the curtain. As a result sometimes a solution, or at least a good idea will emerge apparently out of nowhere. A period of concerted effort to check the idea and put it in a form that is understandable to others is then necessary. Poincaré’s contemporary Albert Einstein may have expressed this most succintly when he said that “Creativity is the residue of time wasted”.
There seems to be a ceaseless effort to increase productivity in all disciplines, yet at some level this effort may be counterproductive. Creativity is essential to many jobs. And it seems that our mind needs freedom and distraction to be creative.
Notes: Here is Poincare’s description of creativity http://www.is.wayne.edu/drbowen/crtvyw99/poincare.htm. Here is an interesting call to lessen our productivity http://www.nytimes.com/2012/05/27/opinion/sunday/lets-be-less-productive.html?_r=1, and here is how longer work weeks do not necessarily translate into extra value for employers http://www.salon.com/2012/03/14/bring_back_the_40_hour_work_week/