Brain Pickings

French Polymath Henri Poincaré on How Creativity Works

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How to spark the “sudden illumination” of creative genius.

In his fantastic 1939 Technique for Producing Ideas, James Webb Young extolled “unconscious processing” — a period marked by “no effort of a direct nature” toward the objective of your creative pursuit — as the essential fourth step of his five-step outline of the creative process. The idea dates back to William James, who coined the concept of fringe consciousness. T. S. Eliot called this mystical yet vital part of creativity “idea incubation,” which Malcolm Cowley echoed in the second stage of his anatomy of the writing process. John Cleese similarly stressed the importance of time in creative work.

From French polymath and pioneering mathematician Henri Poincaré — whose famous words on the nature of invention inspired the survey that gave us a glimpse of how Einstein’s genius works — comes a fascinating testament to the powerful role of this unconscious incubation in the creative process. In a chapter titled “Mathematical Creation” from his 1904 tome The Foundations of Science: Science and Hypothesis, the Value of Science, Science and Method (public library; free download), Poincaré observes a process profoundly applicable not only to mathematics, but to just about any creative discipline:

I wanted to represent these functions by the quotient of two series; this idea was perfectly conscious and deliberate; the analogy with elliptic functions guided me. I asked myself what properties these series must have if they existed, and succeeded without difficulty in forming the series I have called thetafuchsian.

Just at this time, I left Caen, where I was living, to go on a geologic excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go some place or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidian geometry. I did not verify the idea; I should not have had time, as, upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for conscience’ sake, I verified the result at my leisure.

With a true scientist’s insistence on empirical evidence, Poincaré ensures this was a pattern rather than mere one-off coincidence by citing another example of the process at work:

I turned my attention to the study of some arithmetical questions apparently without much success and without a suspicion of any connection with my preceding researches. Disgusted with my failure, I went to spend a few days at the seaside and thought of something else. One morning, walking on the bluff, the idea came to me, with just the same characteristics of brevity, suddenness and immediate certainty, that the arithmetic transformations of indefinite ternary quadratic forms were identical with those of non-Euclidian geometry.

He puts forth a notion contemporary researchers on creative productivity have since affirmed and speaks to the value of what we too tragically term “procrastination,” which is in fact a valuable part of ideation:

Most striking at first is this appearance of sudden illumination, a manifest sign of long, unconscious prior work. The role of this unconscious work in mathematical invention appears to me incontestable, and traces of it would be found in other cases where it is less evident. Often when one works at a hard question, nothing good is accomplished at the first attack. Then one takes a rest, longer or shorter, and sits down anew to the work. During the first half-hour, as before, nothing is found, and then all of a sudden the decisive idea presents itself to the mind. It might be said that the conscious work has been more fruitful because it has been interrupted and the rest has given back to the mind its force and freshness.

What’s more, Poincaré observes, not only circumstances but also substances help prime the mind for such moments of “sudden illumination”:

One evening, contrary to my custom, I drank black coffee and could not sleep. Ideas rose in crowds; I felt them collide until pairs interlocked, so to speak, making a stable combination. It seems, in such cases, that one is present at his own unconscious work, made partially perceptible to the over-excited consciousness, yet without having changed its nature. Then we vaguely comprehend what distinguishes the two mechanisms or, if you wish, the working methods of the two egos.

Still, Poincaré is careful to point out that without a foundation of prior conscious work — something Alexander Flexner touched on in his timeless meditation on the usefulness of useless knowledge — these “sudden illuminations” wouldn’t take place:

There is another remark to be made about the conditions of this unconscious work: it is possible, and of a certainty it is only fruitful, if it is on the one hand preceded and on the other hand followed by a period of conscious work. These sudden inspirations (and the examples already cited sufficiently prove this) never happen except after some days of voluntary effort which has appeared absolutely fruitless and whence nothing good seems to have come, where the way taken seems totally astray. These efforts then have not been as sterile as one thinks; they have set agoing the unconscious machine and without them it would not have moved and would have produced nothing.

He concludes:

The subliminal self is in no way inferior to the conscious self; it is not purely automatic; it is capable of discernment; it has tact, delicacy; it knows how to choose, to divine. What do I say? It knows better how to divine than the conscious self, since it succeeds where that has failed.

It appears, then, that in order for us to lubricate the machinery of unconscious ideation, we have to first prime the mind with directed conscious work, then relieve it of its standard inhibitions, whether by a distracting situation like a trip or a vacation, or by a stimulating substance like caffeine. (Curoiusly, more than a century after Poincaré’s remarks, scientists are beginning to suspect caffeine has the opposite effect and cramps creativity by making us too focused.)

Complement Poincaré’s insights from The Foundations of Science with Young’s indispensable 5-step “technique” for ideation and this excellent contemporary field guide to creativity.

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