Now Pasteur was well acquainted with Jenner's work. To quote one of his biographers, Dr. Dubos (himself an eminent biologist): 'Soon after the beginning of his work on infectious diseases, Pasteur became convinced that something similar to "vaccination" was the best approach to their control. It was this conviction that made him perceive immediately the meaning of the accidental experiment with chickens.'
In other words, he was 'ripe' for his discovery, and thus able to pounce on the first favourable chance that offered itself. As he himself said: 'Fortune favours the prepared mind.' Put in this way, there seems to be nothing very awe-inspiring in Pasteur's discovery. Yet for about three-quarters of a century 'vaccination' had been a common practice in Europe and America; why, then, did nobody before Pasteur hit on the 'obvious' idea of extending vaccination from smallpox to other diseases? Why did nobody before him put two and two together? Because, to answer the question literally, the first 'two' and the second 'two' appertained to different frames of reference. The first was the technique of vaccination; the second was the hitherto quite separate and independent research into the world of micro-organisms: fowl-parasites, silkworm-bacilli, yeasts fermenting in wine-barrels, invisible viruses in 'the spittle of rabid dogs. Pasteur succeeded in combining these two separate frames because he had an exceptional grasp of the rules of both, and was thus prepared for the moment when chance provided an appropriate link.
He knew -- what Jenner knew not -- that the active agent in Jenner's 'vaccine' was the microbe of the same disease against which the subject was to be protected, but a microbe which in its bovine host had undergone some kind of 'attenuation'. And he further realized that the cholera bacilli left to themselves in the test-tubes during the whole summer had undergone the same kind of 'attenuation' or weakening, as the pox bacilli in the cow's body. This led to the surprising, almost poetic, conclusion, that life inside an abandoned glass tube can have the same debilitating effect on a bug as life inside a cow. From here on the implications of the Gloucestershire dairymaid's statement became gloriously obvious: 'As attenuation of the bacillus had occurred spontaneously in some of his cultures [just as it occurred inside the cow], Pasteur became convinced that it should be possible to produce vaccines at will in the laboratory. Instead of depending upon the chance of naturally occurring immunizing agents, as cow-pox was for smallpox, vaccination could then become a general technique applicable to all infectious diseases.' [9]
One of the scourges of humanity had been eliminated -- to be replaced in due time by another. For the story has a sequel with an ironic symbolism, which, though it does not strictly belong to the subject, I cannot resist telling. The most famous and dramatic application of Pasteur's discovery was his anti-rabies vaccine. It was tried for the first time on a young Alsatian boy by name ofJosef Meister, who had been savagely bitten by a rabid dog on his hands, legs, and thighs. Since the incubation period of rabies is a month or more, Pasteur hoped to be able to immunize the boy against the deadly virus which was already in his body. After twelve injections with rabies vaccine of increasing strength the boy returned to his native village without having suffered any ill effects from the bites. The end of the story is told by Dubos: 'Josef Meister later became gatekeeper at the Pasteur Institute in Paris. In 1940, fifty-five years after the accident that gave him a lasting place in medical history, he committed suicide rather than open Pasteur's burial crypt for the German invaders.' [9a] He was evidently predestined to become a victim of one form of rabidness or another.
Now for a discovery of a diametrically opposite kind, where intuition plays the dominant part. The extracts which follow are from a celebrated lecture by Henri Poincaré at the Societé de Psychologie in Paris, and concern one of his best-known mathematical discoveries: the theory of the so-called 'Fuchsian functions'. To reassure the reader I hasten to quote from Poincaré's own introductory remarks:
I beg your pardon; I am about to use some technical expressions, but they need not frighten you for you are not obliged to understand them. I shall say, for example, that I have found the demonstration of such a theorem under such circumstances. This theorem will have a barbarous name unfamiliar to many, but that is unimportant; what is of interest for the psychologist is not the theorem but the circumstances. . . .
And now follows one of the most lucid introspective accounts of the Eureka act by a great scientist:
For fifteen days I strove to prove that there could not be any functions like those I have since called Fuchsian functions. I was then very ignorant; every day I seated myself at my work table, stayed an hour or two, tried a great number of combinations, and reached no results. One evening, contrary to my custom, I drank black coffee and could not sleep. Ideas rose in crowds; I felt them collide until pairs interlocked, so to speak, making a stable combination. By the next morning I had established the existence of a class of Fuchsian functions, those which come from the hypergeometric series; I had only to write out the results, which took but a few hours. Then I wanted to represent these functions by the quotient of two series; this idea was perfectly conscious and deliberate, the analogy with elliptic functions guided me. I asked myself what properties these series must have if they existed, and I succeeded without difficulty in forming the series I have called theta-Fuchsia. Just at this time I left Caen, where I was then living, to go on a geologic excursion under the auspices of the school of mines. The changes of travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go some place or other. At the moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. I did not verify the idea; I should not have had time, as, upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for conscience' sake I verified the result at my leisure. Then I turned my attention to the study of some arithmetical questions apparently without much success and without a suspicion of any connection with my preceding researches. Disgusted with my failure, I went to spend a few days at the seaside, and thought of something else. One morning, walking on the bluff, the idea came to me, with just the same characteristics of brevity, suddenness, and immediate certainty, that the arithmetic transformations of indeterminate ternary quadratic forms were identical with those of non-Euclidean geometry. Returned to Caen, I meditated on this result and deduced the consequences. The example of quadratic forms showed me that there were Fuchsian groups other than those corresponding to the hyper-geometric series; I saw that I could apply to them the theory of theta-Fuchsian series and that consequently there existed Fuchsian functions other than those from the hypergeometric series, the ones I then knew. Naturally I set myself to form all these functions. I made a systematic attack upon them and carried all the outworks, one after another. There was one, however, that still held out, whose fall would involve that of the whole place. But all my efforts only served at first the better to show me the difficulty, which indeed was something. All this work was perfectly conscious. Thereupon I left for Mont-Valérien, where I was to go through my military service; so I was very differently occupied. One day, going along the street, the solution of the difficulty which had stopped me suddenly appeared to me. I did not try to go deep into it immediately, and only after my service did I again take up the question. I had all the elements and had only to arrange them and put them together. So I wrote out my final memoir at a single stroke and without difficulty.
I shall limit myself to this single example; it is useless to multiply them. In regard to my other researches I would have to say analogous things . . .
Most striking at first is this appearance of sudden illumination, a manifest sign of long, unconscious prior work. The role of this unconscious work in mathematical invention appears to me incontestable. . . . [10]
Similar experiences have been reported
by other mathematicians. They seem to be the rule rather than the exception. One of them is Jacques Hadamard: [11]
. . . One phenomenon is certain and I can vouch for its absolute certainty: the sudden and immediate appearance of a solution at the very moment of sudden awakening. On being very abruptly awakened by an external noise, a solution long searched for appeared to me at once without the slightest instant of reflection on my part -- the fact was remarkable enough to have struck me unforgettably -- and in a quite different direction from any of those which I had previously tried to follow.
A few more examples. André Marie Ampère (1775-1836), after whom the unit of electric current is named, a genius of childlike simplicity, recorded in his diary the circumstances of his first mathematical discovery:
On April 27, 1802, he tells us, I gave a shout of joy . . . It was seven years ago I proposed to myself a problem which I have not been able to solve directly, but for which I had found by chance a solution, and knew that it was correct, without being able to prove it. The matter often returned to my mind and I had sought twenty times unsuccessfully for this solution. For some days I had carried the idea about with me continually. At last, I do not know how, I found it, together with a large number of curious and new considerations concerning the theory of probability. As I think there are very few mathematicians in France who could solve this problem in less time, I have no doubt that its publication in a pamphlet of twenty pages is a good method for obtaining a chair of mathematics in a college. [12]
The memoir did in fact get him a professorship at the Lycée in Lyon. It was called Considerations of the Mathematical Theory of Games of Chance, and demonstrated, among other things, that habitual gamblers are, in the long run, bound to lose.
Another great mathematician, Karl Friedrich Gauss, described in a letter to a friend how he finally proved a theorem on which he had worked unsuccessfully for four years:
At last two days ago I succeeded, not by dint of painful effort but so to speak by the grace of God. As a sudden flash of light, the enigma was solved. . . . For my part I am unable to name the nature of the thread which connected what I previously knew with that which made my success possible. [13]
On another occasion Gauss is reported to have said: 'I have had my solutions for a long time, but I do not yet know how I am to arrive at them.' Paraphrasing him, Polya -- a contemporary mathematician -- remarks: 'Wlien you have satisfied yourself that the theorem is true, you start proving it.' [14]
We have seen quite a few cats being let out of the bag -- the mathematical mind, which is supposed to have such a dry, logical, rational texture. As a last example in this chapter I shall quote the dramatic case of Friedrich August von Kekulé, Professor of Chemistry in Ghent, who, one afternoon in 1865, fell asleep and dreamt what was probably the most important dream in history since Joseph's seven fat and seven lean cows:
I turned my chair to the fire and dozed, he relates. Again the atoms were gambolling before my eyes. This time the smaller groups kept modestly in the background. My mental eye, rendered more acute by repeated visions of this kind, could now distinguish larger structures, of manifold conformation; long rows, sometimes more closely fitted together; all twining and twisting in snakelike motion. But look! What was that? One of the snakes had seized hold of its own tail, and the form whirled mockingly before my eyes. As if by a flash of lightning I awoke . . . Let us learn to dream, gentlemen. [15]
The serpent biting its own tail gave Kekulé the clue to a discovery which has been called 'the most brilliant piece of prediction to be found in the whole range of organic chemistry' and which, in fact, is one of the cornerstones of modern science. Put in a somewhat simplified manner, it consisted in the revolutionary proposal that the molecules of certain important organic compounds are not open structures but closed chains or 'rings' -- like the snake swallowing its tail.
Summary
When life presents us with a problem it will be attacked in accordance with the code of rules which enabled us to deal with similar problems in the past. These rules of the game range from manipulating sticks to operating with ideas, verbal concepts, visual forms, mathematical entities. When the same task is encountered under relatively unchanging conditions in a monotonous environment, the responses will become stereotyped, flexible skills will degenerate into rigid patterns, and the person will more and more resemble an automaton, governed by fixed habits, whose actions and ideas move in narrow grooves. He may be compared to an engine-driver who must drive his train along fixed rails according to a fixed timetable.
Vice versa, a changing, variable environment will tend to create flexible bchaviour -- patterns with a high degree of adaptability to circumstances -- the driver of a motor-car has more degrees of freedom than the engine-driver. But novelty can be carried to a point -- by life or in the laboratory -- where the situation still resembles in some respects other situations encountered in the past, yet contains new features or complexities which make it impossible to solve the problem by the same rules of the game which were applied to those past situations. When this happens we say that the situation is blocked -- though the subject may realize this fact only after a series of hopeless tales, or never at all. To squeeze the last drop out of the metaphor: the motorist is heading for a frontier to which all approaches are barred, and all his skill as a driver will not help him -- short of turning his car into a helicopter, that is, playing a different kind of game.
A blocked situation increases the stress of the frustrated drive. What happens next is much the same in the chimparizee's as in Archimedes's case. When all hopeful attempts at solving the problem by traditional methods have been exhausted, thought runs around in circles in the blocked matrix like rats in a cage. Next, the matrix of organized, purposeful behaviour itself seems to go to pieces, and random trials make their appearance, accompanied by tantrums and attacks of despair -- or by the distracted absent-mindedness of the creative obsession. That absent-mindedness is, of course, in fact single-mindedness; for at this stage -- the 'period of incubation' -- the whole personality, down to the unverbalized and unconscious layers, has become saturated with the problem, so that on some level of the mind it remains active, even while attention is occupied in a quite different field -- such as looking at a tree in the chimpanzee's case, or watching the rise of the water-level; until either chance or intuition provides a link to a quite different matrix, which bears down vertically, so to speak, on the problem blocked in its old horizontal context, and the two previously separate matrices fuse. But for that fusion to take place a condition must be fulfilled which I called 'ripeness'.
Concerning the psychology of the creative act itself, I have mentioned the following, interrelated aspects of it: the displacement of attention to something not previously noted, which was irrelevant in the old and is relevant in the new context; the discovery of hidden analogies as a result of the former; the bringing into consciousness of tacit axioms and habits of thought which were implied in the code and taken for granted; the uncovering of what has always been there.
This leads to the paradox that the more original a discovery the more obvious it seems afterwards. The creative act is not an act of creation in the sense of the Old Testament. It does not create something out of nothing; it uncovers, selects, re-shuffles, combines, synthesizes already existing facts, ideas, faculties, skills. The more familiar the parts, the more striking the new whole. Man's knowledge of the changes of the tides and the phases of the moon is as old as his observation that apples fall to earth in the ripeness of time. Yet the combination of these and other equally familiar data in Newton's theory of gravity changed mankind's outlook on the world.
'It is obvious', says Hadamard, 'that invention or discovery, be it in mathematics or anywhere else, takes place by combining ideas. . . . The Latin verb cogito for to think etymologically means "to shake together". St. Augustine had already noticed that and also observed that intelligo means to select among.'
The 'ripeness' of a c
ulture for a new synthesis is reflected in the recurrent phenomenon of multiple discovery, and in the emergence of similar forms of art, handicrafts, and social institutions in diverse cultures. But when the situation is ripe for a given type of discovery it still needs the intuitive power of an exceptional mind, and sometimes a favourable chance event, to bring it from potential into actual existence. On the other hand, some discoveries represent striking tours de force by individuals who seem to be so far ahead of their time that their contemporaries are unable to understand them.
Thus at one end of the scale we have discoveries which seem to be due to more or less conscious, logical reasoning, and at the other end sudden insights which seem to emerge spontaneously from the depth of the unconscious. The same polarity of logic and intuition will be found to prevail in the methods and techniques of artistic creation. It is summed up by two opposite pronouncements: Bernard Shaw's 'Ninety per cent perspiration, ten per cent inspiration', on the one hand, Picasso's 'I do not seek -- I find' (je ne cherche pas, je trouve), on the other.
VI
THREE ILLUSTRATIONS
Before proceeding further, let me return for a moment to the basic, bisociative pattern of the creative synthesis: the sudden interlocking of two previously unrelated skills, or matrices of thought. I shall give three somewhat more detailed examples which display this pattern from various angles: Gutenberg's invention of printing with movable types; Kepler's synthesis of astronomy and physics; Darwin's theory of evolution by natural selection.