[G.Polya]
Subconscious
work. One evening I wished to discuss
with a friend a certain author but I could not remember
the author's name. I was annoyed, because I remembered
fairly well one of his stories. I remembered also some
story about the author himself which I wanted to tell; I
remembered, in fact, everything except the name. Repeatedly,
I tried to recollect that name occurred to me
without any effort.
The reader, very likely, remembers some similar experience
of his own. And, if he is a passionate problem-solver,
he has probably had some similar experience with
problems. It often happens that you have no success at
all with a problem; you work very hard yet without finding
anything. But when you come back to the problem
after a night's rest, or a few days' interruption, a bright
idea appears and you solve the problem easily. The
nature of the problem matters little; a forgotten word,
a difficult word from a crossword-puzzle, the beginning
of an annoying letter, or the solution of a mathematical
problem may occur in this way.
Such happenings give the impression of subconscious
work. The fact is that a problem, after prolonged absence,
may return into consciousness essentially clarified
much nearer to its solution than it was when it dropped
out of consciousness. Who clarified it, who brought it
nearer to the solution? Obviously, oneself, working at it
subconsciously It is difficult to give any other answer;
although psychologists have discovered the beginnings
of another answer which may turn out some day to be
more satisfactory.
Whatever may or may not be the merits of the theory
of subconscious work, it is certain that there is a limit
beyond which we should not force the conscious reflection.
There are certain moments in which it is better to
leave the problem alone for awhile. "Take counsel of
your pillow" is an old piece of advice. Allowing an interval
of rest to the problem and to ourselves, we may
obtain more tomorrow with less effort. "if today will not,
tomorrow may" is another old saying. But it is desirable
not to set aside a problem to which we wish to come back
later without the impression of some achievement; at
least some little point should be settled, some aspect of
the question somewhat elucidated when we quit working.
Only such problems come back improved whose solution
we passionately desire, or for which we have worked
with great tension; conscious effort and tension seem to
be necessary to set the subconscious work going. At any
rate, it would be too easy if it were not so; we could
solve difficult problems just by sleeping and waiting for
a bright idea.
Past ages regarded a sudden good idea as an inspiration,
a gift of the gods. You must deserve such a gift by
work, or at least by a fervent wish.10(footnote:
for an all-round discussion of "unconscious thinking" see
Jacques Hadamard, The Psychology of Invention in the
Mathematical Field.