(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.