Copernicus, Kepler, Galileo, Freud -- I have quoted only a few outstanding
examples of mental eye-cataract. How often did Archimedes get into his
bath and watch the rising water-level which gave a perfect measure
of the volume of his gnarled body? We must resign ourselves to the
fact that snowblindness is inherent in the human condition; if it were
not so, then everything we know today about the theory of numbers, or
analytical geometry, would have been discovered within a few generations
after Euclid.
Gradual Integrations
In some of the discoveries which I discussed earlier on, a sudden
intuition sparked off the instant fusion of previously unrelated
matrices. In the cases described in the previous section the spark
failed to ignite. In yet other cases it initiates the fusion without
completing it. Loewi could not decipher the note relating to his dream,
and had to dream a second time before he accepted its message. Kepler
rejected the 'truth of Nature', and only admitted it when it returned 'by
the backdoor'. Some of Köhler's less gifted chimpanzees discovered,
unaided, various new techniques for making and using tools -- then seemed
to forget them again; but on the next test they rediscovered them after
a much shorter period of trying than the first time (See Book Two,
XIII
). The human equivalent of this situation is a cry
of distress: 'Blast it, I had the solution, but now I have forgotten
it again.'
Cases of this kind make one think of a lighter whose wick has started to
glow, without properly burning. The struggle will have to go on, and more
sparks will have to be produced, before it bursts into flame. In other
words, intuition has established some tentative link between the two
distant frames of reference, but that link is insufficient to overcome
resistances and effect their fusion. It will have to be strengthened by
repetition (as in the case of Loewi) or else additional links will have
to be discovered to precipitate the integration.
The Dawn of Language
The most common example for this type of gradual process is the way in
which the child discovers that 'all things have names'. During the first
year of its life, the average baby progresses from spontaneous babbling
to the imitative repetition of syllables and words spoken by adults --
with some vague intimations that these words are somehow connected with
the situation in which they are regularly used. It seems that eager
parents frequently teach their offspring its first words by a process
of repetitive 'stamping in', at an age when the baby is not yet ripe
to grasp the principles involved. Thus Watson conditioned an infant
to say 'da' whenever it was given the bottle, starting at five months,
twenty days -- that is, six months earlier than the first words normally
appear. The process took more than three weeks, at the end of which the
word 'da' became the first, mechanically established llnk between the
two otherwise still unrelated matrices of 'sounds' and 'things'.
With each month that passes, the acquisition of new word-links becomes
quicker and easier; the child is 'learning to learn'; until, usually
in the second half of the second year, it 'makes the most important
discovery of its whole life --
that everything has a name
'. [13]
As far as one can generalize from the scant statistics, the vocabulary
of the average child at the close of the first year is three words; at
eighteen months twenty-two words. This seems to be the approximate age
when the 'naming discovery' is made, for three months later the average
vocabulary has jumped to a hundred and eighteen:
SMITH'S TEST [14]
Average size of vocabularies
-----------------------------------------------------------
Age Number of cases reported Number of words
-----------------------------------------------------------
-- 8 13 0
--10 17 1
1--0 52 3
1--3 19 19
1--4 14 22
---- ---
1--9 14 118
2--0 25 272
2--4 14 446
3--0 20 896
3--6 26 1222
4--0 26 1540
4--6 32 1870
5--0 20 2072
5--6 27 2289
6--0 9 2562
___________________________________________________________
The integration of the matrices is indicated not only by the steep rise of
the learning curve after the eighteenth month, but by the fact that from
now on the child, of its own initiative, will point at a thing and ask
to be told its name. Delighted with its discovery, it sometimes develops
a veritable 'naming mania': it indicates an object, calls out its name,
or, if it has forgotten it, invents a name of its own; for henceforth a
person or thing is felt to be incomplete if it has no name attached to it.
Thus the dawn of symbol-consciousness is a gradual, cumulative event;
a kind of diluted Eureka process, spread out in time, because the final
integration can take place only when the child's mental organization
has attained sufficient maturity. But the same process may occur
in a telescoped, highly dramatized form in rare cases such as Helen
Keller's. The blind, deaf, and mute little girl was nearly seven when Miss
Sullivan took charge of her and taught her the first few words, c-a-k-e,
d-o-l-l, etc., by means of the manual alphabet, a kind of morse spelt
by finger-play. Since Helen was 'overripe' for learning a language, she
covered, within less than a month, the same ground which takes a normal
child about two years, from the imitative acquisition of the first word
('I did not know that I was spelling a word or even that words existed;
I was simply making my fingers go in monkey-like imitation') -- to the
final discovery:
We walked down the path to the well-house, attracted by the fragrance
of the honeysuckle with which it was covered. Some one was drawing
water and my teacher placed my hand under the spout. As the cool stream
gushed over one hand she spelled into the other the word 'water,' first
slowly, then rapidly. I stood still, my whole attention fixed upon the
motions of her fingers. Suddenly I felt a misty consciousness as of
something forgotten -- a thrill of returning thought; and somehow the
mystery of language was revealed to me. I knew then that 'w-a-t-e-r'
meant the wonderful cool something that was flowing over my hand. That
living word awakened my soul, gave it light, joy, set it free! . . .
I left the well-house eager to learn. Everything had a name, and each
name gave birth to a new thought. As we returned to the house each
object that I touched seemed to quiver with life. That was because I
saw everything with the strange new sight that had come to me. [15]
Here we have the undiluted bisociative act, the sudden synthesis of the
universe of signs and the universe of things. In its sequel each matrix
imparts a new significance, a new dimension to the other: the words begin
to 'live', to 'give birth to new thoughts'; and the objects begin to
'quiver' under the touch of the magic wand of language.
Helen Keller's dramatic moment of truth is quite unlike the gradual dawn
of the name-relation in normal children, and much closer to the sudden
insight in discoveries of the type of Pasteur's. The normal child'
s naming discovery could be likened to the process known in logic as
empirical induction
: 'some things have names ergo I assume that
all things have names'. (Needless to say, I do not mean to impute any
conscious reasoning of this kind to the babe in its cradle.) The chick
episode, on the other hand, which made Pasteur jump to his conclusion
and establish the general principle of immunization, could be called
'induction from a single case' -- a procedure usually illustrated in
primers on logic by the example 'all French waiters have red hair'. For
a detailed discussion of the relations of gradual learning to sudden
discovery I must refer the reader to Book Two.
Summary
New integrations arise by various processes which can be arranged in a
series. It ranges from faulty or premature integrations, through partial
blindness towards the meaning and significance of one's own discoveries,
to the gradual blending of matrices by dint of repetitive experiences,
which increase the number of links between them. Finally, there is the
sudden illumination of 'spontaneous' discoveries, sparked off by an
unconscious intuition, or a chance observation, or a combination of both.
X
THE EVOLUTION OF IDEAS
There is a theory, put forward by Henry Sarton, and held to be
self-evident by many scientists, which says, broadly speaking, that
the history of science is the only history which displays a cumulative
progress of knowledge; that, accordingly, the progress of science is
the only yardstick by which we can measure the progress of mankind;
and moreover, that the word 'progress' itself has no clearly defined
meaning in any field of activity -- except the field of science.
This is the kind of pronouncement where it is advisable to hold one's
breath and count to ten before expressing indignant protest or smug
agreement, according to one's allegiance to eggheads or engineers.
Personally I believe that there is a grain of truth in Sarton's
proposition -- but no more than that.
Separations and Reintegrations
There are certain analogies between the characteristic stages in the
history of an individual discovery, and the historical development of a
branch of science as a whole. Thus a 'blocked matrix' in the individual
mind reflects some kind of impasse into which a science has manoeuvred
itself. The 'period of incubation', with its frustrations, tensions,
random tries, and false inspirations, corresponds to the critical
periods of 'fertile anarchy' which recur, from time to time, in the
history of every science. These crises have, as we saw, a destructive
and a constructive aspect. In the case of the individual scientist,
they involve a temporary retreat to some more primitive form of ideation
-- innocence regained through the sacrifice of hard-won intellectual
positions and established beliefs; in the case of a branch of science
taken as a whole, the crisis manifests itself in a relaxation of the rigid
rules of the game, a thawing of the collective matrix, the breakdown
of mental habits and absolute frontiers -- a process of "reruler pour
mieux sauter" on an historic scale. The Eureka act proper, the moment
of truth experienced by the creative individual, is parallaled on the
collective plane by the emergence, out of the scattered fragments,
of a new synthesis, brought about by a quick succession of individual
discoveries -- where, characteristically, the same discovery
is often made by several individuals, at the same time
(cf.
p. 110
f).
The last stage -- verification, elaboration, consolidation -- is by far
the least spectacular, the most exacting, and occupies the longest periods
of time both in the life of the individual and in the historical evolution
of science. Copernicus picked up the ancient Pythagorean teaching of
the sun as the centre of all planetary motions when he was a student
in Renaissance Italy (where the idea was much discussed at the me), and
spent the rest of his life elaborating it into a system. Darwin hit on
the idea of evolution by natural selection at the age of twenty-nine; the
remaining forty-four years of his life were devoted to its corroboration
and exposition. Pasteur's life reads like a story divided into several
chapters. Each chapter represents a period which he devoted to one field
of research; at the beginning of each period stands the publication of a
short preliminary note which contained the basic discovery in a nutshell;
then followed ten or fifteen years of elaboration, consolidation,
clarification.
The collective advances of science as a whole, and of each of its
specialized branches, show the same alternation between relatively brief
eruptions which lead to the conquest of new frontiers, and long periods of
consolidation. In the case of the individual, this protracted chore has
its natural limits at three score years and ten, or thereabouts; but on
the historical stage, the assimilation, consolidation, interpretation, and
elaboration of a once revolutionary discovery may go on for generations,
and even centuries. The new territory opened up by the impetuous advance
of a few geniuses, acting as a spearhead, is subsequently occupied
by the solid phalanxes of mediocrity; and soon the revolution turns
into a new orthodoxy, with its unavoidable symptoms of one-sidedness,
over-specialization, loss of contact with other provinces of knowledge,
and ultimately, estrangement from reality. We see this happening --
unavoidably, it seems -- at various times in the history of various
sciences. The emergent orthodoxy hardens into a 'closed system' of
thought, unwilling or unable to assimilate new empirical data or to
adjust itself to significant changes in other fields of knowledge;
sooner or later the matrix is blocked, a new crisis arises, leading to
a new synthesis, and the cycle starts again.
This does not mean, of course, that science does not advance; only that
it advances in a jerky, unpredictable, 'unscientific' way. Although
'in the year 1500 Europe knew less than Archimedes who died in the year
212 B.C.',[1] it would nevertheless be foolish to deny that today we
know considerably more than Archimedes. And I mean by that not only the
fantastic and threatening achievements of applied science which have
transformed this planet to a point where it is becoming increasingly
uninhabitable; but that we also know more than Archimedes in other, more
worthwhile ways, by having gained deeper insights into the structure
of the universe, from the spiral nebulae to the acid molecules which
govern heredity.