Chasing Insight is Hard and Joyful Work

(This article was written for and appears in the IATEFL-Hungary (International Association of Teachers of English as a Foreign Language) journal "Melting Pot" for December 2012.)

In a well-known story, Archimedes, asked to determine whether or not a crown was made of gold or of a cheaper alloy, could not destroy the crown to assay it. So how could he determine whether or not the crown was pure or alloy? Imagine him puzzling over this apparently insoluble problem. Then, watching the way his body displaced water as he lowered himself into a bathtub, the answer struck him. He is said to have exclaimed, “Eureka,” “I have found (it).”

He realized that if the crown and an equal weight of gold displaced equal amounts of water, then the crown was genuine. If the crown displaced more water than an equal weight of gold, then it was at least partly made of a less dense, less valuable material—say, silver.

This story is supposed to demonstrate the lightning-like swiftness of insight, granted to geniuses like Archimedes, but, perhaps, not to you and me. Some research in creativity focuses on such “ah hah” moments. But there’s a lot more to it than this, and the research of eminent scholars like the late Howard Gruber focuses on the context in which such moments of discovery occur. (One of his books is appropriately called Creative People at Work.) (For the purposes of this article, I am using the word “insight” when I could use, variously, “imagination” or “inspiration.”)

Some of the following points are worth stating because, however obvious they may be, they are essential and instructive.

First, Archimedes stated the problem clearly for himself—or had it stated for him. Honing our questions so that we understand what we are asking and so that we are asking about things that really matter to us put us on the path to insight.

Second, however brilliant he may have been—and he was probably among the more brilliant humans ever to live—Archimedes had a store of knowledge and experience, an education or self-education, perhaps acquired over years, at least about things like the differing densities of metals and about water in bathtubs. You simply can’t have insights about matters of which you are ignorant. And, very often, insight comes in recognizing a solution to a problem in one area—the purity of metals—with an insight in an apparently unrelated area—displacing water in a bathtub. A broad and deep education—not necessarily schooling, but education—provides the background from which insight may arise.

Third, Archimedes chose to live with the possibility that there was an answer to his problem, and that he could discover it. Some problems have solutions that are only discovered years or even centuries after they are first posed. Some problems, perhaps, have no solutions. Regardless, if we do not approach problems with the understanding that they may be solved, we are unlikely to garner any insight.

Fourth, Archimedes spent time puzzling over this new problem, working on it, we don’t know for how long. Picture him staring at the crown, hefting it in his hands. Picture him exhausting what he knew about such matters. How many days or weeks passed while the obdurate crown sat there, untested? Insight is generally granted to those who exert themselves, not to those who seek instant gratification.

Fifth, he let the problem go. Minimally, he decided to take a bath. History is full of insights granted to those who take a walk, go to church, doodle in the sand, plow a field, lie back in a bedroom watching a fly, pick burrs off a dog, or simply take a bus or streetcar home. [In order, those who received inspiration or insight on these occasions are Beethoven, Silver (the Post-It), Woodland (the barcode), Farnsworth (TV), Descartes (Cartesian plane), de Mestral (Velcro), Kekule (chemical structures), and Einstein (mass-energy equivalency).]

Sixth, Archimedes had and recognized an insight. Chances are good we each have several insights per day, although of a lower order than Archimedes’, but neglect to recognize them, to write them down, or to pay attention to them.

Seventh, he recognized the truth of his solution even before he had worked out the details and put it to the test. This is common—that a researcher will recognize a solution, or a composer will “see” a symphony whole—even though it may take weeks, months, or even years to demonstrate the solution to a problem or to complete the written score.

It could easily have been the case, for example, that even though Archimedes knew he was correct, he was unable to prove it—if the difference in the amounts of water displaced was too small to measure using his antique equipment, for instance. In that case, he would have had to invent some new, more sensitive balance, conduct several trials, and think things through to eliminate error. But all of this thinking and work come after the moment of insight.

[We don’t know exactly how Archimedes solved the problem, what method or apparatus he used. A simple solution available to him was to balance the crown with an equal weight of gold in air and then transfer the balance, gold, crown and all, into a tank of water. If the crown and the gold unbalanced under water, he could conclude that their densities were different and that the crown was not pure.]

Eighth, we assume, he was willing to do the work necessary to prove that his insight was right, and not content simply to sit in a taverna and hold forth on his (untested) brilliance.

Ninth, he did the work, successfully. (He could have been willing but unsuccessful, leaving it for later generations to prove him right.)

Insight, then—which we may also call at least a lower form of inspiration—is one moment within a larger context of inquiry and meaning. It is the pivot, we could say, between the work that leads up to it and the work that follows and tests it.

Is it possible to generate insight, or does it just strike, like lightning? Perhaps we should discuss this question in terms of probability. Is it possible to increase the probability that we may, through insight, solve the problems life poses us?

Let’s examine Archimedes’ story with this in mind. If he was unlearned and ignorant of concepts of density and displacement, he could not have solved the problem. If he was unwilling to tackle the problem, for any reason—laziness, an assessment of its difficulty—he could not have solved it.

Harder to appreciate, perhaps, if he had not taken a bath, he would have been less likely to solve it. (It’s possible that he could have chained himself to his desk, endless cups of coffee at his elbow, and simply thought of a bathtub, but life and history tell us that this simply isn’t a good way to solve problems that require insight.) After an effort to understand and solve the problem, he moved on to other, more practical matters. He stood up and moved. Possibly, he “slept on it,” perhaps for more than one night.

He was open to the possibility that a mundane matter, like taking a bath, could illuminate a seemingly unrelated matter, like comparing gold with alloy.

He trusted his judgment—when he had an insight, he recognized it.

And he was willing not merely to let the solution waft through his mind, but to do the work necessary afterward to put it to the test, to prove it in the real world. We don’t know much about how Archimedes actually accomplished this, but we know from the experience of others that such insights, however immediately they strike us, can take weeks or months to engineer into real-world solutions.

If we focus only on “eureka” or “ah hah” moments, then we run the risk of removing genius to a realm beyond that of we mere mortals. If we are too egocentric, we may wait, with increasing frustration, for insights that don’t materialize—or we may mistake our fevered daydreams for true insights.

If we focus, however, on the education and work that lead, potentially, to insight, and recognize the work required to implement and test insight once attained, we are more likely to gather insights of our own. And we are less likely to mistake illusion for insight.

The pursuit of insight may seem like a take-it-or-leave-it proposition. Life is fine as it is, so I don’t need insight and the hard work it entails.

It’s not so simple, however.

All knowledge, in the end, is the result of insight; if not our own, then someone else’s. When we were young and eager and curious and flexible, we gathered insights all the time and thought nothing of it (sort of like the way we stopped at nothing to learn to walk, despite failing for months and months, falling and falling. If we had to accomplish something so physically demanding today, would we do it? Or would we simply rationalize our lack of motivation as inability?). When we were children, it was how we formed a picture of the world.

As we age, we tend to calcify, to ossify, to become less playful, less open to insight. But we needn’t let this change overcome us. Although it’s hard work to pursue insight, the path is clear, and it’s a joyful one, too—so joyful that Archimedes, possessed by the joy of his insight, was said to have jumped out of his bath and run naked through the streets of Syracuse.