But they translated this prophetic intuition into a premature synthesis between 'things' and 'numbers', based on the assumption that a line consisted of a definable number of tiny dots, a plane of a definable number of these lines, and so on. They soon discovered, however, that the length of a line such as the diagonal of a square cannot be defined by any countable number of dots; one can draw the diagonal in a jiffy, but to write down the number defining its length one would have to use an infinite series of decimals. To make the scandal worse, numbers of this kind could be shown to be neither even nor odd -- or both. Pythagoreans called these numbers arrhetos, unspeakable (we call them, more politely, irrational numbers), and tried to keep their existence secret, because they were convinced that their assertion of a harmonious mathematical order behind the untidy world of appearances was true and correct; when a member of the Brotherhood, Hippasos, let the secret leak out, he was reportedly put to death. The failure of this premature attempt at a synthesis brought the quantitative approach to nature into discredit. The physics of Aristotle, which ruled Europe for two thousand years, paid no attention to quantity or measurement; physics remained divorced from mathematics until the scientific revolution in the seventeenth century A.D. brought them together again.
Another premature synthesis, which I have already mentioned, was the Keplerian cosmology, in which the sun sweeps the lazy planets round their orbits with invisible heavenly brooms. But, in this case, the error was a fertile one: physics and astronomy, once 'shaken together' even though in the wrong way, could never again be separated. Equally fertile was the alchemists' right intuition, supported by wrong arguments, of the transmutability of chemical elements. On the other hand, the phrenology of Franz Josef Gall had the opposite effect. Gall thought that every mental faculty is seated in a definite region on the surface of the brain, and that a person's abilities and character could be assessed by the bumps on his skull. It was the first, premature, and naïve attempt to correlate psychology with brain-physiology. Though phrenology was highly fashionable around A.D. 1800, it brought such discredit in its wake that for a century or more psychologists would have nothing to do with speculations about the structure and function of the brain.
Thus the premature integration of matrices which are not yet sufficiently consolidated has in some cases a wholesome effect, by stimulating more mature attempts in the same direction; while in other cases it acts as a deterrent and carries the stigma of superstition or 'un-scientific thinking'. Taken in a wider sense, the category of premature intuitions accommodates the whole body of folk-wisdom -- herbal knowledge, weather-lore, psychosomatic healing by hypnosis, suggestion, shock, and abreaction -- down to Jenner's diarymaid who 'would not take the pox'. We have learned to recognize in these intuitive insights and techniques the forerunners of our more mature discoveries and rediscoveries; and we thus arrive at a progression in several stages. In the first stage the two matrices which will participate in the ultimate synthesis are tentatively and inadequately joined together by the logic of the unconscious. In the second the haphazard connection is severed again, and a reaction may set in which keeps them apart for a considerable time. In the final stage, after the definite merger, the previously separate matrices become mentally inseparable, and we marvel at our former blindness.
Snowblindness
'The mind', wrote Wilfred Trotter, 'likes a strange idea as little as the body likes a strange protein and resists it with similar energy. It would not perhaps be too fanciful to say that a new idea is the most quickly acting antigen known to science. If we watch ourselves honestly we shall often find that we have begun to argue against a new idea even before it has been completely stated.' [5]
I shall not dwell on the martyrology of genius; the title of this section refers to that remarkable form of blindness which often prevents the original thinker from perceiving the meaning and significance of his own discovery. Jealousy apart, the anti-body reaction directed against new ideas seems to be much the same whether the idea was let loose by others -- or oneself. The defence mechanisms which protect habits against the intrusion of novelty accounts both for our mental inertia -- and mental stability.
Copernicus was an orthodox believer in the physics of Aristotle, and stubbornly clung to the dogma that all heavenly bodies must move in perfect circles at uniform velocities. In the fourth chapter of the Third Book of the Revolutions of the Heavenly Spheres, the original manuscript of the book contains the following lines:
It should be noticed, by the way, that if the two circles have different diameters, other conditions remaining unchanged, then the resulting movement will not be a straight line but . . . what mathematicians call an ellipse. (my italics)
This is actually not true, for the resulting curve will be a cycloid resembling an ellipse -- but the odd fact is that Copernicus had hit on the ellipse which is the form of all planetary orbits -- had arrived at it for the wrong reasons and by faulty deduction -- and having done so, promptly dropped it: the passage is crossed out in the manuscript, and is not contained in the printed edition of the Revolutions. The history of human thought is full of triumphant eurekas; but only rarely do we hear of the anti-climaxes, the missed opportunities, which leave no trace.
Kepler, too, nearly threw away the elliptic orbits; for almost three years he held the solution in his hands -- without seeing it. His conscious mind refused to accept the 'cartload of dung' which the underground had cast up. When the battle was over, he confessed: 'Why should I mince my words? The truth of Nature, which I had rejected and chased away, returned by stealth through the backdoor, disguising itself to be accepted. Ah, what a foolish bird I have been!' [6]
Poor Kepler, he was even more foolish than he thought: he actually discovered universal gravity -- then rejected it. In the Preface to the New Astronomy he explains that the tides are due to the attraction of the moon, and describes the working of gravity -- even that the attracting force is proportionate to mass; but in the text of that book, and of all subsequent works, he has -- incredible as it sounds -- completely forgotten all about it. I have given elsewhere a detailed account of this remarkable case of snowblindness. [7]
Galileo revolutionized astronomy by the use of the telescope; but he refused to believe in the reality of comets and declared them to be optical illusions. For he too believed that heavenly bodies must move in perfect circles; and since comets moved in very elongated elliptical orbits, they could not be heavenly bodies.
Freud's revered master, Professor Brucke at the Vienna Medicine Faculty, discovered, in 1849, a technique to illuminate the retina of the eye; but the idea of observing the illuminated retina through a lens did not occur to him! It was his friend Helmholtz who hit on the idea -- while preparing a lecture on Brucke's work -- and thus became the inventor of the ophthalmoscope.
Freud himself had two narrow escapes, as it were, from achieving world fame in his twenties. In the course of his physiological researches at Brucke's Institute 'he was trembling on the very brink of the important neurone theory, the basis of modern neurology'; but, as Ernest Jones said, 'in the endeavour to acquire "discipline" he had not yet perceived that in original scientific work there is an equally important place for imagination'. [8] It is strange indeed to hear the founder of psychoanalysis being accused by his pupil and biographer of having in his early years suffered from lack of imagination; but there it is -- and worse to come.
The fantastic character of the 'Cocaine Episode' in Freud's life can be appreciated only by comparing the silences in Freud's autobiography with the revelations in Jones's biography. In the spring of 1884, Freud -- then twenty-eight -- read in a German medical paper that an Army doctor had been experimenting 'with cocaine, the essential constituent of coca leaves which some Indian tribes chew to enable them to resist privations and hardships'. He ordered a small quantity of the stuff from a pharmaceutical firm, tried it on himself, his sisters, fiancée, and patients, decided that cocaine was a 'magical drug', which procured 'the most gorge
ous excitement', left no harmful after-effect, and was not habit-forming! In several publications he unreservedly recommended the use of cocaine against depression, indigestion, 'in those functional states comprised under the name of neurasthenia', and during the withdrawal-therapy of morphine addicts; he even tried to cure diabetes with it. 'I am busy', he wrote to his future wife, 'collecting the literature for a song of praise to this magical substance.' One is irresistibly reminded of Aldous Huxley's songs of praise to mescaline; but Huxley was neither a member of the medical profession nor the founder of a new school in psychotherapy.
Two years after the publication of his first paper on the wonder-drug, Knapp, the great American ophthalmologist, greeted Freud 'as the man who had introduced cocaine to the world', and congratulated him on the achievement. In the same year, 1886, however, cases of cocaine addiction and intoxication were being reported from all over the world, and in Germany there was a general alarm. . . . [9] The man who had tried to benefit humanity or at all events to create a reputation by curing "neurasthenia" was now accused of unleashing evil on the world.' Among Freud's personal patients one died as a result of a large dose of the drug; another -- his close friend Fleishl -- whom he tried to cure from morphine addiction, became cocaine-addicted instead, and developed 'a delirium tremens with white snakes creeping over his skin'. [10] A leading neurologist, Erlenmeyer, described cocaine as 'the third scourge of humanity' -- the other two being alcohol and morphine. [11]
I have said enough about the disasters of this episode. And yet Freud's dabbling with cocaine became a blessing to humanity -- but not in the way in which he had thought of it. Two of his colleagues at the Medical Faculty, Koller and Koenigstein, both ophthalmologists, both of incomparably smaller stature than Freud, read his 1884 paper, experimented with cocaine, and saw almost at once what Freud's snowblindness prevented him from seeing. Freud was not interested in surgery; it did not enter into his habits of thought. He was fascinated by the possible internal uses of cocaine, and, above all, its effects on nervous disorders. Only in the final paragraph of his paper did he casually mention some possible 'additional uses' of cocaine as a pain-deadener in local infections; its uses as an anesthetic in minor surgery never occurred to him. He and Koller both noticed that after swallowing cocaine their mouths and lips went numb -- the familiar sensation after the dentist's injection. Koller took the hint -- Freud did not. Freud suggested to Koenigstein that cocaine could be used to alleviate the pain in certain eye-diseases; but it was Koenigstein who thought of using it as an anaesthetic in eye-operations. Among the first of these, incidentally, was an operation on Freud's father for glaucoma -- carried out by Koenigstein, with Koller administering the cocaine, and Freud assisting. . . .
But even at that stage Freud still considered the tremendous benefits of local anaesthetics as merely 'one more of the outlying applications of which his beloved drug was capable. It took a long time before he could assimilate the bitter truth that Koller's use of it was to prove practically the only one of value and all the rest dust and ashes.' [12]
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 wa
s 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.