Some of us, very methodical in
solving problems, get from A to Z in 25 diligently organized steps. Others get there in intuitive leaps,
from A to K, then to Q, then to Z, perhaps backtracking a bit along the way when
confused. Neither process is
definitively better, for methodical and intuitive people can be equally
creative and successful in working things through.
I am reminded of the two sons of good friends of mine—call
the older S1 and the younger S2. S1 is systematic in the way he tackles tasks,
S2 is instinctive. Many
years ago, when S1 was about 10 or 11, he got a new computer for
Christmas. As he unpacked it, he
immediately went to the instruction manual, not only to check whether all the
components were there, but to prepare to assemble them. S2, three years younger,
simply started to plug the parts together and had the computer operational
before S1 was even a few pages into the manual. The two are equally smart. I used to fault S1 when he
wrote an essay because he would assemble more information than he needed to
sustain his theme. I used to fault
S2 because he left out convincing arguments that were obvious to
him, although maybe not to his audience.
I am one of those who likes eventually to visit every letter
in the alphabet. If I make an
intuitive leap over some of them to enhance my understanding and project my
path to Z, I then force myself to go back and systematically fill in the gaps
to verify that my intuition hasn't led me astray. That used to drive my late wife Helen crazy. If I'd gotten an answer intuitively,
she would wonder, why did I waste time shoring up the result analytically? For her, intuitive leaps sufficed.
I most assuredly endorse intuition as a method of attacking
a problem, especially if it is preliminary to deeper investigation. One of my postings in March, Intuition
and Expertise, was indeed an essay in
praise of it. However, as I said
then, I believe that intuition must be informed by expertise, and expertise
comes only through arduous practice.
A chessmaster can in a flash intuit the course of a game many moves in
advance by just glancing at the board, yet only because of years of hard
effort. An amateur's intuitive
move is likely a mere stab in the dark.
Even my friends' son S2 assembled that computer so quickly
because he had spent years of his earlier youth plugging electrical circuits
together just for the fun of it, so he knew what made sense.
Helen would also complain when I carefully plotted a route
through a strange country, usually planning a fast, minimum-distance drive
along autoroutes: A to Z in a trice!
"Why not wander along byways and get lost?" she would
say. "Maybe we'll see some
lovely, unexpected sights. We are, after all, tourists!" Impatient as I habitually was to get to
Z, I still had to admit that she had a point, at least for tourism. When she prevailed over my sense of
efficiency, we often did come across beautiful vistas, towns, churches and the
like. It's what I call discovery
by meandering.
Transposed to problem solving, discovery by meandering—in a
usually vain hope for serendipity—is an ineffective heuristic. I liken it to jumping through the
alphabet at random, guided neither by method nor intuition, placing one's faith
in a stroke of luck. Even then,
one must have a well-honed ability to recognize luck when stumbling upon it, an ability that is itself part of
intuition. Without it, an amateur
chess player may miss a lucky opportunity in front of his eyes. Being truly lucky is largely a matter
of preparing one's intuition to take advantage of Fortune when she smiles, not
of simply praying that she does.
In my earlier posting on intuition, I described a grand old
professor of mine at MIT, Professor Ernst Guillemin, a master of the intuitive
method of teaching and learning. I
remember his presenting a paper at a symposium at a time when younger members
of his field had turned toward proving results through methodical sequences of
theorems. He said, "I'm not
going to try to present a series of theorems and lemmas to get to my results—I
wouldn't know how. But I'm pretty
sure that I will be able to convince you of my results by showing you how
intuitively reasonable they are."
And he did. Because he was
a grandmaster with decades of experience, he likely knew that his results were
correct because his brain had flashed through all the intermediate steps
subconsciously. And even if he
stumbled on a result by sheer luck, he immediately intuitively recognized its
worth.
Few of us are purely methodical or purely intuitive; most
are a combination of the two.
Although some at the intuitive extreme, like Professor Guillemin, will
be inclined to leave it to others to fill in the gaps to their satisfaction,
most will themselves backfill with careful analysis. Those toward the methodical extreme will usually be
unsatisfied with a result unless it also appeals to their intuition. I like to think that I fall about
halfway along the spectrum, mixing intuition and method in equal measures.
Were Helen alive today, I imagine she would disagree with my
self-assessment, instead placing me squarely among those who address life systematically
at every step. Luckily for me,
that's probably one of the reasons I was able to catch her in the first place—I
guess she intuitively wanted someone she could count on to methodically conduct
our affairs. If so, it was a good
trade-off, for I much needed the spontaneity she brought me, which I now sorely
miss.