Archimedes
Let me illustrate the last point by a human discovery which has much in common with Sultan's: the Principle of Archimedes. I must tell the story in a somewhat simplified form.
Hiero, tyrant of Syracuse and protector of Archimedes, had been given a beautiful crown, allegedly of pure gold, but he suspected that it was adulterated with silver. He asked Archimedes's opinion. Archimedes knew, of course, the specific weight of gold -- that is to say, its weight per volume unit. If he could measure the volume of the crown he would know immediately whether it was pure gold or not; but how on earth is one to determine the volume of a complicated ornament with all its filigree work? Ah, if only he could melt it down and measure the liquid gold by the pint, or hammer it into a brick of honest rectangular shape, or . . . and so on. At this stage he must have felt rather like Nueva, flinging herself on her back and uttering whimpering sounds because the banana was out of her grasp and the road to it blocked.
Blocked situations increase stress. Under its pressure the chimpanzee reverts to erratic and repetitive, random attempts; in Archimedes's case we can imagine his thoughts moving round in circles within the frame of his geometrical knowledge; and finding all approaches to the target blocked, returning again and again to the starting point. This frustrating situation, familiar to everybody trying to solve a difficult problem, may be schematized as in the following diagram, where 'S' represents the starting point, the loops are trains of thought within the blocked matrix, and 'T' represents the target (that is: 'a method of measuring the volume of the crown') -- which, unfortunately, is located outside the plane of the matrix.
One day, while getting into his bath, Archimedes watched absent-mindedly the familiar sight of the water-level rising from one smudge on the basin to the next as a result of the immersion of his body, and it occurred to him in a flash that the volume of water displaced was equal to the volume of the immersed parts of his own body -- which therefore could simply be measured by the pint. He had melted his body down, as it were, without harming it, and he could do the same with the crown.
Once more, as in the case of the chimpanzee, the matter is childishly simple after the fact -- but let us try to put ourselves in Archimedes's place. He was in the habit of taking a daily bath, but the experiences and ideas associated with it moved along habit-beaten tracks: the sensations of hot and cold, of fatigue and relaxation, and a pretty slave-girl to massage his limbs. Neither to Archimedes nor to anybody else before him had it ever occurred to connect the sensuous and trivial occupation of taking a hot bath with the scholarly pursuit of the measurement of solids. No doubt he had observed many times that the level of the water rose whenever he got into it; but this fact, and the distance between the two levels, was totally irrelevant to him -- until it suddenly became bisociated with his problem. At that instant he realized that the amount of rise of the water-level was a simple measure of the volume of his own complicated body.
The discovery may now be schematized as follows (Figure 8):
M1 is the same as in the preceding diagram, governed by the habitual rules of the game, by means of which Archimedes originally tried to solve the problem; M2 is the matrix of associations related to taking a bath; m2 represents the actual train of thought which effects the connection. The Link L may have been a verbal concept (for instance: 'rise of water-level equals melting down of my solid body'); it may equally well have been a visual impression in which the water-level was suddenly seen to correspond to the volume of the immersed parts of the body and hence to that of the crown -- whose image was constantly lurking on the fringe of his consciousness. The essential point is, that at the critical moment both matrices M1 and M2 were simultaneously active in Archimedes's mind -- though presumably on different levels of awareness. The creative stress resulting from the blocked situation had kept the problem on the agenda even while the beam of consciousness was drifting along quite another plane. Without this constant pressure, the favourable chance-constellation would have passed unnoticed -- and joined the legion of man's missed opportunities for a creative departure from the stale habits of thought which numb his mental powers.
The sequel to the discovery is well known; because of its picturesque appeal I shall occasionally refer to discovery in its psychological aspect as the 'Eureka process' or 'Eureka act'.
Let us look at Archimedes's discovery from a different angle. When one climbs into a bath one knows that the water-level will rise owing to its displacement by the body, and that there must be as much water displaced as there is body immersed; moreover, one mechanically estimates the amount of water to be let into the bath because of this expectation. Archimedes, too, must have known all this -- but he had probably never before verbalized, that is, consciously formulated that bit of knowledge. Yet implicitly it was there as part of his mental equipment; it was, so to speak, included in the code of rules of bath-taking behaviour. Now we have seen that the rules which govern the matrix of a skill function on a lower level of awareness than the actual performance itself -- whether it is playing the piano, carrying on a conversation, or taking a bath. We have also seen that the bisociative shock often has the effect of making such implicit rules explicit, of suddenly focussing awareness on aspects of experience which had been unverbalized, unconsciously implied, taken for granted; so that a familiar and unnoticed aspect of a phenomenon -- like the rise of the water-level -- is suddenly perceived at an unfamiliar and significant angle. Discovery often means simply the uncovering of something which has always been there but was hidden from the eye by the blinkers of habit.
This equally applies to the discoveries of the artist who makes us see familiar objects and events in a strange, new, revealing light -- as if piercing the cataract which dims our vision. Newton's apple and Cézanne's apple are discoveries more closely related than they seem.
Chance and Ripeness
Nearly all of Köhler's chimpanzees sooner or later learned the use of implements, and also certain methods of making implements. But a dog, however skilful in carrying a stick or a basket around, will never learn to use the stick to get a piece of meat placed outside its reach. We might say that the chimpanzees were ripe to discover the use of tools when a favourable chance-opportunity presented itself -- such as a stick lying around just when needed. The factors which (among others) constitute ripeness for this type of discovery are the primates' manual dexterity and advanced oculo-motor co-ordination, which enable them to develop the playful habit of pushing objects about with branches and sticks. Each of the separate skills, whose synthesis constitutes the new discovery, was well established previously and frequently exercised. In a similar way Archimedes's mental skill in manipulating abstract concepts like volume and density, plus his acute powers of observation, even of trivia, made him 'ripe' for his discovery. In more general terms: the statistical probability for a relevant discovery to be made is the greater the more firmly established and well exercised each of the still separate skills, or thought-matrices, are. This explains a puzzling but recurrent phenomenon in the history of science: that the same discovery is made, more or less at the same time, by two or more people; and it may also help to explain the independent development of the same techniques and similar styles of art in different cultures.
Ripeness in this sense is, of course, merely a necessary, not a sufficient, condition of discovery. But it is not quite such an obvious concept as it might seem. The embittered controversies between different schools in experimental psychology about the nature of learning and understanding can be shown to derive to a large extent from a refusal to take the factor of ripeness seriously. The propounders of Behaviouristic psychology were wont to set their animals tasks for which they were biologically ill-fitted, and thus to prove that new skills could be acquired only through conditioning, chaining of reflexes, learning by rote. Köhler and the Gestalt school, on the other hand, set their chimpanzees tasks for which they were ripe or almost ripe, to prove that all learning was based on insight. The
contradictory conclusions at which they arrived need surprise us no more than the contrast between the learning achievements of a child of six months and a child of six years. This is a necessarily over-simplified description (for a detailed treatment see Book Two, XII); the only point I wish to make is that the more ripe a situation is for the discovery of a new synthesis, the less need there is for the helping hand of chance.
Archimedes's eyes falling on the smudge in the bath, or the chimpanzee's eyes falling upon the tree, are chance occurrences of such high probability that sooner or later they were bound to occur; chance plays here merely the part of triggering off the fusion between two matrices by hitting on one among many possible appropriate links. We may distinguish between the biological ripeness ofa species to form a new adaptive habit or acquire a new skill, and the ripeness of a culture to make and to exploit a new discovery. Hero's steam engine could obviously be exploited for industrial purposes only at a stage when the technological and social conditions made it both possible and desirable. Lastly (or firstly), there is the personal factor -- the role of the creative individual in achieving a synthesis for which the time is more or less ripe.
The emphasis is on the 'more or less'. If ripeness were all -- as Shakespeare and the Marxist theory affirm -- the role of genius in history would be reduced from hero to midwife, who assists the inevitable birth; and the act of creation would be merely a consummation of the preordained. But the old controversy whether individuals make or are made by history acquires a new twist in the more limited field of the history of science. The twist is provided by the phenomenon of multiple discoveries. Historical research into this curious subject is of fairly recent origin; it came as a surprise when, in 1922, Ogburn and Thomas published some hundred and fifty examples of discoveries and inventions which were made independently by several persons; and, more recently, Merton came to the seemingly paradoxical conclusion that 'the pattern of independent multiple discoveries in science is . . . the dominant pattern rather than a subsidiary one'. [5] He quotes as an example Lord Kelvin, whose published papers contain 'at least thirty-two discoveries of his own which he subsequently found had also been made by others'. The 'others' include some men of genius such as Cavendish and Helmholtz, but also some lesser lights.
The endless priority disputes which have poisoned the supposedly serene atmosphere of scientific research throughout the ages, and the unseemly haste of many scientists to establish priority by rushing into print -- or, at least, depositing manuscripts in sealed envelopes with some learned society -- point in the same direction. Some -- among them Galileo and Hooke -- even went to the length of publishing half-completed discoveries in the form of anagrams, to ensure priority without letting rivals in on the idea. Köhler's chimpanzees were of a more generous disposition.
Thus one should not underestimate ripeness as a factor facilitating discoveries which, as the saying goes, are 'in the air' -- meaning, that the various components which will go into the new synthesis are all lying around and only waiting for the trigger-action of chance, or the catalysing action of an exceptional brain, to be assembled and welded together. If one opportunity is missed, another will occur.
But, on the other hand, although the infinitesimal calculus was developed independently by Leibniz and by Newton, and a long line of precursors had paved the way for it, it still required a Newton or a Leibniz to accomplish the feat; and the greatness of this accomplishment is hardly diminished by the fact that two among millions, instead of one among millions, had the exceptional genius to do it. We are concerned with the question how they did it -- the nature of creative originality -- and not with the undeniable, but trivial consideration that if they had not lived somebody else would have done it some time; for that leaves the same question to be answered, to wit, how that someone else did it. I shall not presume to guess whether outstanding individuals such as Plato and Aristotle, Jesus of Nazareth and Paul of Tarsus, Aquinas, Bacon, Marx, Freud, and Einstein, were expendable in the above sense, so that the history of ideas in their absence would have taken much the same course -- or whether it is the creative genius who determines the course of history. I merely wish to point out that some of the major break-throughs in the history of science represent such dramatic tours de force, that 'ripeness' seems a very lame explanation, and 'chance' no explanation at all. Einstein discovered the principle of relativity 'unaided by any observation that had not been available for at least fifty years before'; [6] the plum was overripe, yet for half a century nobody came to pluck it. A less obvious example is Everist Galois, one of the most original mathematicians of all times, who was killed in an absurd duel in 1832, at the age of twenty. In the night before the duel he revised a paper to the Académie des Sciences (which had previously rejected it as unintelligible); then, in a letter to a friend, he hurriedly put down a number of other mathematical discoveries. 'It was only after fifteen years, that, with admiration, scientists became aware of the memoir which the Academy had rejected. It signifies a total transformation of higher algebra, projecting a full light on what had been only glimpsed thus far by the greatest mathematicians . . .' [7] Furthermore, in the letter to his friend, Galois postulated a theorem which could not have been understood by his contemporaries because it was based on mathematical principles which were discovered only a quarter century after his death. 'It must be admitted,' another great mathematician commented, 'first, that Galois must have conceived these principles in some way; second, that they must have been unconscious in his mind since he makes no allusion to them, though they by themselves represent a significant discovery).' [8]
This leads us to the problem of the part played by unconscious processes in the Eureka act.
Pythagoras, according to tradition, is supposed to have discovered that musical pitch depends on the ratio between the length of vibrating chords -- the starting point of mathematical physics -- by passing in front of the local blacksmith on his native island of Samos, and noticing that rods of iron of different lengths gave different sounds under the blacksmith's hammer. Instead of ascribing it to chance, we suspect that it was some obscure intuition which made Pythagoras stop at the blacksmith's shop. But how does that kind of intuition work? Here is the core ofthe problem of discovery -- both in science and in art.
Logic and Intuition
I shall briefly describe, for the sake of contrast, two celebrated discoveries of entirely different kinds: the first apparently due to conscious, logical reasoning aided by chance; the second a classic case of the intervention of the unconscious.
Eighteen hundred and seventy-nine was the birth-year of immunology -- the prevention of infectious diseases by inoculation. By that time Louis Pasteur had already shown that cattle fever, rabies, silkworm disease, and various other afflictions were caused by micro-organisms, and had firmly established the germ theory of disease. In the spring of 1879 -- he was fifty-seven at that time -- Pasteur was studying chicken cholera. He had prepared cultures of the bacillus, but for some reason this work was interrupted, and the cultures remained during the whole summer unattended in the laboratory. In the early autumn, however, he resumed his experiments. He injected a number of chickens with the bacillus, but unexpectedly they became only slightly ill and recovered. He concluded that the old cultures had been spoilt, and obtained a new culture of virulent bacilli from chickens afflicted by a current outbreak of cholera. He also bought a new batch of chickens from the market and injected both lots, the old and the new, with the fresh culture. The newly bought chicks all died in due time, but, to his great surprise, the old chicks, who had been injected once already with the ineffective culture, all survived. An eye-witness in the lab described the scene which took place when Pasteur was informed of this curious development. He remained silent for a minute, then exclaimed as if he had seen a vision: "Don't you see that these animals have been vaccinated!"
Now I must explain that the word 'vaccination' was at that time already a century old. It is derived from vacca, cow. Some time
in the 1760s a young medical student, Edward Jenner, was consulted by a Gloucester dairymaid who felt out of sorts. Jenner thought that she might be suffering from smallpox, but she promptly replied: 'I cannot take the smallpox because I have had the cow-pox.' After nearly twenty years of struggle against the scepticism and indifference of the medical profession, Jenner succeeded in proving the popular belief that people who had once caught the cow-pox were immune against smallpox. Thus originated 'vaccination' -- the preventive inoculation of human beings against the dreaded and murderous disease with material taken from the skin sores of afflicted cattle. Although Jenner realized that cow-pox and smallpox were essentially the same disease, which became somehow modified by the organism which carried it, he did not draw any general conclusions from his discovery. 'Vaccination' soon spread to America and became a more or less general practice in a number of other countries, yet it remained limited to smallpox, and the word itself retained its exclusively bovine connotations.
The vision which Pasteur had seen at that historic moment was, once again, the discovery of a hidden analogy: the surviving chicks of the first batch were protected against cholera by their inoculation with the 'spoilt' culture as humans are protected against smallpox by inoculation with pox bacilli in a modified, bovine form.
The Act of Creation Page 11