In a great book, “Hare Brain Tortoise Mind”, the author, Guy Claxton, writes on intuition.

‘Did you make that song up?’

‘Well, I sort of made it up,’ said Pooh. ‘It isn’t Brain

. . . but it comes to me sometimes.’

‘Ah,’ said rabbit, who never let things come to him,

But always went and fetched them.

-A. A. Milne, The House at Pooh Corner

“In his autobiography the nineteenth-century English philosopher Herbert Spencer recounts a conversation with his friend Mary Ann Evans - the novelist George Eliot. They had been discussing Spencer's recently published book Social Statics, and George Eliot suddenly observed that, given the amount of thinking he must have done, his forehead remained remarkably unlined. ‘I suppose it is because I am never puzzled,’ said Spencer - to which Eliot, understandably, replied that this was the most arrogant remark she had ever heard. Spencer says that he went on to justify his remark by explaining that

my mode of thinking does not involve the concentrated effort which is commonly accompanied by wrinkling of the brows. The conclusions, at which I have from time to time arrived . . . have been arrived at unawares - each as the ultimate outcome of a body of thoughts that slowly grew from a germ. . . Lime by lime, in unobtrusive ways, without conscious intention or appreciable effort, there would grow up a coherent and organised theory. Habitually the process was one of slow unforced development, often extending over years; and it was, I believe, because the thinking done went on in this gradual, almost spontaneous way, without strain, that there was an absence of those lines of thought which Miss Evans remarked.

In Spencer's opinion 'a solution reached in the way described is more likely to be true than one reached in pursuance of a determined effort to find a solution. The determined effort causes perversion of thought. . . An effort to arrive forthwith at some answer to a problem acts as a distorting factor in consciousness and causes error, whereas a quiet contemplation of the problem from time to time allows those proclivities of thought which have probably been caused unawares by experience, to make themselves felt, and to guide the mind to the right conclusion.’

The ways of knowing with which both Pooh Bear and Herbert Spencer are familiar are different from d-mode in a number of ways. Most obviously, they take time, and therefore they require patience: a relaxed, unhurried, unanxious approach to problems. In this they resemble 'learning by osmosis', but they are not the same. In learning by osmosis, the undermind gradually uncovers patterns that are embedded in, or distributed across, a wide variety of experiences. Know-how is distilled from the residue of hundreds of specific instances and events. But while Spencer's insights into the organisation of society undoubtedly drew on much prior thought and observation, the process that he is referring to is one that goes beyond this unconscious distillation. This process seems to reflect not the acquisition of new information so much as the mind's ability to discover, over time, new patterns or meanings within the information which it already possesses, and to register these consciously as insight or intuition. Though experience provides the data, the process is not acquisitive but ruminative. Pooh's song that prompted Rabbit's question demonstrates the same process on a smaller scale. He was not announcing the inductive discovery of a new generalisation, but simply producing something which came 'out of the blue'.

Despite the widely-held assumption that d-mode represents the most powerful thinking tool we possess - which makes it the one we call. upon, or revert to, in the face of urgent demands for solutions - the truth is that our ideas, and often our best, most ingenious ideas, do not arrive as the result of faultless chains of reasoning. They 'occur to us'. They 'pop into our heads'. They come out of the blue. When we are relaxed we operate very largely by intuition. We don't usually offer a detailed rationale for our restaurant preference: we say ‘I feel like Thai’. We happily allow ourselves to be nudged by feelings and impulses that do not come with an explicit justification. Yet when we are put 'on the spot' in a meeting, or are faced with an urgent 'problem' that demands 'solution', we may act as if these promptings were weak, unreliable or negligible. We feel as if intuition will not stand up to scrutiny, and will not bear much weight. There is now a body of research which shows that intuition is more valuable and more trustworthy than we think; and that we disdain it, when we are 'on duty', to our practical detriment.

We need a more accurate understanding of the nature and status of intuition: one which neither under nor overvalues it. Those who disparage intuition are reacting, often unwittingly, against the presumption that intuition constitutes a form of knowledge that is 'higher' than mere reason, or even infallible. The dictionary definitions still carry some of that inflated view, and by doing so they create expectations that are patently false. Chambers' dictionary gives intuition as 'the power of the mind by which it immediately perceives the truth of things, without reasoning or analysis'. The Shorter Oxford is more poetic and more presumptuous still: it gives intuition as 'the immediate knowledge ascribed to angelic and spiritual beings, with whom vision and knowledge are identical'. Now while it may be the case that there is a certain quality of intuition, one which may take much careful cultivation to acquire, which does give access to a qualitatively different kind of knowledge, it is self-evident that everyday intuition falls far short of this ideal. Our promptings are notoriously fallible, whether they concern a career move or a life partner, a book that we misjudged by its cover or a new route that the 'nose' confidently said was a short cut, but which only succeeded in getting us lost.

Intuitions can be wrong, but that does not mean they are worthless. Intuitions are properly seen as 'good guesses'; hunches or hypotheses thrown up by the undermind which deserve serious, but not uncritical, attention. They offer an overall 'take' on a situation that manifests not - not yet - as a reasoned analysis, but as an inkling or an image. Behind the scenes, the undermind may have integrated into this tangible prompt a host of different considerations, including analogies to past experience and aspects of the present situation, of which the conscious mind may not have even been aware. And this integration can happen, as the dictionary definitions say, 'immediately', or it may take time - even, as in Spencer's case, up to years. But the result, when it does 'pop up', is always provisional. It is a pudding, served up by the unconscious, whose proof is in the eating: a critical testing which may be the reaction of the audience to an impromptu witticism, a la Pooh, the rigorous checking of logical implications, or the detailed working out of a creative poetic or artistic theme.

Fast intuitions - 'snap judgements' and quick reactions - are vital responses for the human being, just as they are for animals. When the present event is a variation on a familiar theme, it pays to be able to classify it and react in habitual fashion. To spend time pondering on insignificant details is sometimes wasteful, or even dangerous. No need to inspect the number plate of the bus as it bear down upon you. But these reflexes work to our detriment when a new situation looks similar to ones we have experienced in the past, but is actually different. Then the balance of priorities shifts, and it is now the quick, stereotyped response that is the risky one, while more leisurely scrutiny can pay dividends.

The importance of this shift from fast to slow thinking was graphically demonstrated in the laboratory by Abraham and Edith Luchins as long ago as the 1950s. They set people puzzles of the following sort. 'Imagine that you are standing beside a lake, and that you are given three empty jars of different sizes. The first jar holds 17 pints of water; the second holds 37 pints; and the third holds 6 pints. Your job is to see whether, using these three jars, you can measure out exactly 8 pints.' After some thought (which may, to start with, be quite logical), most people are able to end up with 8 pints in the largest jar. Then they are set another problem of the same type, except this time the jars hold respectively 31, 61 and 4 pints, and the target is to get 22 pints. And then another, with jars holding 10, 39 and 4 pints where the target is 21 pints. (You may like to try to solve these puzzles before consulting the notes for the solutions.) You will find that the same strategy will work for all three problems. But now comes the critical shift. You are next given jars of capacity 23, 49 and 3 pints, and asked to make 20 pints. If you have stopped thinking, and are now applying your new-found rule mindlessly, you will solve the problem - but you will not spot that there is now a much simpler solution. The problem looks the same, but this particular one admits of two solutions, one of which is more elegant and economical than the other.

We can easily imagine a business company - or any other kind of organisation - falling into the same trap. They may 'think they are thinking' about each problem as it comes along; but if they are unable to think freshly, they will keep coming up with the same kinds of answers - even when circumstances have changed and new possibilities are there to be discovered. And one of the strongest forces that prevents the discovery of these new avenues may be the habit of thinking fast: of taking your first intuitive assessment of the situation for granted, and not bothering to stop and check. Milton Rokeach tested this hypothesis, using the Luchins jars, by forcing people to slow down when they were looking at the new problems. If they were allowed to give the 'solution' in their own time, most people immediately applied the rule that had worked previously without question. But when they were prevented from writing down their answer for a minute, some of them pondered the problem in greater detail - and were able to discover the new solution.

Not surprisingly, this benefit only accrued to people who did actually attend to the details of the new problem during the delay. Many people reported that they made up their minds quickly about the answer, and then spent the enforced interval thinking about all kinds of unrelated things - 'making plans for Saturday night's party', 'thinking about letters I had to write', 'counting the holes in the tiles on the ceiling', and so on - and for them, the extra time obviously did nothing to improve their creativity. What was more interesting, however, was the mental activity of the subjects who did find the new solution. They were not earnestly figuring out the answers, or making calculations on bits of scrap paper. They were actually musing in a much more general way on what type of questions were being asked, and what the experimenter was up to. One said, 'I was wondering what the experiment was trying to prove.' Another said, 'I was thinking what the results would indicate.' It was this kind of 'meta-level' questioning that led to the insight, not the disciplined application of procedures.

Let me illustrate how intuition works with the aid of a slightly more complicated example (one, incidentally, that Wittgenstein was fond of using in his philosophy seminars). Imagine that the Earth has been smoothed over so that it forms a perfect sphere, and that a piece of (non-elastic) string has been tied snugly round the equator. Now suppose that the string is untied, and another 2 metres added to the total length, which is then spaced out so that the gap which has been created between the string and the Earth's surface is the same all the way round. How big is this gap? Could you slide a hair under the string? A coin? A paperback book? Could you crawl under it? Most people's strong intuition is that the gap would be tiny, of the order of a millimetre or two at the most. In fact, it is easy to prove mathematically that it is about 32 centimetres, or just over a foot; so you could indeed crawl under the string. (The proof is in the notes, for those who wish to follow it.) The strange thing, when you work out the geometry, is that the size of the gap turns out to be independent of the size of the original sphere (or circle: the problem is not essentially three-dimensional). So you would get the same-sized gap whether you started with a tennis ball, a circus ring, or the universe. Most people's intuition, on the other hand, insists that the larger the original object, the less 'difference' the 2 metre extension is going to make: in other words, the smaller the gap.

Intuition goes awry here because it is based on the unconscious assumption that this situation is analogous to other, apparently similar, situations where the idea that 'the larger the object, the smaller the change' does apply. If we were to change the puzzle slightly, and say: 'Supposing the oceans were neatened up into a huge cylinder, how much would the level rise if we added 20 litres of water?’, then the answer is indeed 'not very much’; and we would be right, in this instance, to assume that the larger the original volume, the smaller the difference to its depth. The 20 litres would make much more difference to the depth of a paddling pool. It just turns out that this plausible assumption works for the height of cylinders, but not for the radius of circles. It is a good guess that in one case turns out to be right, and in the other case wrong. Fast intuitions depend on the undermind taking a quick look at the situation and finding an analogy which seems to offer understanding and prediction. These unconscious analogies surface as intuitions. Whether they are right or not depends not on how 'intuitive' they are, but on the appropriateness of the underlying analogy. Often we are absolutely right. But sometimes the undermind is fooled by appearances, and then it leads us off in the wrong direction.

This example also demonstrates how the way of knowing you employ may give different answers to the very same question. D-mode and intuition may well draw on different processes, knowledge and beliefs, and thus may produce conflicting solutions. If you followed the mathematics in the notes, then you might be rationally persuaded that the gap is a foot, while intuitively you persist in believing it to be minute. Below the surface, some assumptions are being made that lead to one answer. Above the surface, so it seems, different premises lead to a different answer. In this case, it turns out that the 'rational' answer is the right one. In other cases (as when intuition told you that there was something suspicious about the well-spoken woman at the door 'collecting for charity', but you persuaded yourself you were being 'silly') it may be intuition that is right and reason that is wrong. It is an empirical issue.

Which mental mode is engaged - and therefore which answer you get -- may depend on how you happen to be thinking when the question arises; or on some - possibly quite incidental - feature of the situation. If you catch a physics undergraduate in the bar one night and ask her why, when you throw a ball, it moves through an are, she is likely (if she can be bothered) to tell you a story about the 'energy' or 'impetus' you give to the ball when you throw it, and how this gets used up overcoming the drag of the air and the force of gravity. When the upwards 'oomph' has been depleted to a certain level, she says, gravity starts to 'win', the ball reaches its zenith and begins to fall. However, if you then remind her that this is a physics problem, she may well stop for a moment (as she switches from intuitive mode to physicists' d-mode) and say, 'Of course. Silly me. There isn't any "oomph" you put in to the ball as you throw it. The only forces are gravity and the air resistance.' Her first 'take' is an everyday, intuitive one; her second switches her into a different frame of reference, giving access to a different database and different ways of thinking. If the question had been on an examination paper, she would have selected d-mode automatically.

The power of context to flip people into one way of knowing rather than another - and to produce quite different responses to what is logically the same problem - is widespread, and very striking. In a study of ten-year-olds by Ceci and Bronfenbrenner in 1985, for example, the children sat in front of a computer screen in the centre of which one of a variety of geometric shapes would periodically appear. Their job was to predict (by moving the cursor with a mouse) in which direction, and how far, the shape was about to 'jump'. The shapes were circles, squares and triangles that could be dark- or light-coloured, and large or small. In theory, the children could have predicted the jump on the basis of the shape, because squares always went to the right, circles to the left, and triangles stayed in the middle; dark things went up and light things down; and large things went a short distance and small things a long distance. After 750 trials, the children had learnt virtually nothing.

However, after making a small change to the task, which had no effect at all on its logical difficulty, things looked very different. All the experimenters did was replace the three geometrical shapes with animals (birds, bees and butterflies); swap the normal computer cursor for an image of a ‘net’; add some sound effects; and tell the children that this was a game in which they had to try to catch the animals as they moved. After less than half as many goes, all the children were placing the net in the right position to 'capture' the animals with near-perfect accuracy. The geometrical shapes told the children that this was a 'school-type task', and so automatically flipped them into d-mode. They tried to figure out the rules, and couldn't. So they made no progress. The other version led them to reinterpret the display as a ‘video game’ - and this flipped them into an intuitive mode which enabled them to pick up the relevant relationships easily and unconsciously.

Intuitions can also go wrong when they are based on inaccurate judgements about what is relevant and what is not, as we saw earlier with the 'mutilated chessboard'. Here is another example.

A certain town is served by two hospitals. In the larger hospital about 45 babies are born each day, and in the smaller one, about 15. As you know, about 50% of all babies are boys and 50% girls. The exact percentage of girls however naturally varies from day to day. Some days it may be over the 50%; some days under. As a check on this variation, for a period of one year, both of the hospitals recorded the days on which more than 60% of the babies born were girls. Over the year, which hospital do you think recorded more such days? The large one? The small one? Or about the same?

When psychologists Daniel Kahneman and Amos Tversky asked nearly a hundred people this question, 22 per cent said the larger; 22 per cent said the smaller; and 56 per cent said 'about the same’. Nobody sat down and worked it out with a calculator, so we must suppose that all these were intuitions. But more than three-quarters of them were wrong. (I was one of those who said ‘about the same’.) A moment's reflection should be enough, however, to convince you - as it did me - that the correct answer is 'the small one'. The smaller the sample, the easier it is to get a larger percentage skew by chance. (It only takes two 'boys' to turn out to be girls for the small hospital to exceed its 60 per cent point.) A relevant piece of information - the size of the hospital - is actually being tacitly disregarded by half the population when they are generating their intuitive response (even though they are perfectly able to see its relevance when it is pointed out). These 'fast intuitions' are susceptible to all kinds of invisible influences, some of which will be appropriate and beneficial, and others of which will, in a particular instance, be misleading.

If fast intuition is vulnerable when responding to. predicaments that look familiar but which are not as they seem, in what circumstances are the slower ways of knowing of most value? As with learning by osmosis, it turns out that slow intuition is good at uncovering non-obvious relationships between areas of knowledge; at seeing 'the pattern that connects' experiences that are superficially disparate. Intuition proves its worth in any situation that is shadowy, intricate or ill defined - regardless of whether the focus of concern is a mid-life crisis, a knotted-up relationship, an artistic project or a scientific conundrum.

In science, intuition is the faculty that comes up with the metaphor, the image or the idea that binds together and makes sense of experimental results which cumulatively seem to embarrass an existing theory, but which up to that point had lacked any alternative coherence. Both Darwin's account of the mechanism of evolution and Einstein's theories of special and general relativity offered just such explanatory patterns. They took a pile of details and transformed them into a theoretical structure that gave them meaning, and predicted new findings. And these, like many other scientific breakthroughs, came about through a way of knowing that was patient, playful and mysterious, not rational, earnest and explicit. As Einstein himself famously said, of his own creative process:

The words of the language as they are written or spoken do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements of thought are certain signs and more or less clear images which. . . are 'in my case of visual and some of muscular type. These elements take part in a rather vague play. . . in which they can be voluntarily reproduced and combined. . . This combinatory play seems to be the essential feature in productive thought, before there is any connection with logical construction in words or other kinds of sign which can be communicated to others, . . In a stage where words intervene at all, they are, in my case, purely auditive, but they interfere note, ‘interfere’ only in a secondary stage.

Sometimes, as in the case of Herbert Spencer, one is aware of the pattern of thought gradually forming itself, as a large crystalline structure may slowly appear out of a saturated chemical solution in which a seed crystal has been placed. While at other times, the work proceeds unconsciously until the point at which the binding idea as a whole is delivered into consciousness. Rita Levi-Montalcini, who shared the Nobel Prize for medicine in 1986, for example, said: 'You've been thinking about something without willing to for a long time . . . Then, all of a sudden, the problem is opened to you in a flash, and you suddenly see the answer.' While Sir Neville Mott, physics laureate in 1977, confirms both the suddenness of the insight, and the difficulty of finding the right way of expressing it in d-mode: ‘You suddenly see: "It must be like this". That's intuition . . . if you can't convince anybody else. This certainly happened to me in the work for which I got the Nobel prize. It took me years to get my stuff across.'

Intuition may deliver its produce to consciousness in the form of more or less connected and coherent thoughts. But at other times, even for scientists, the undermind speaks in a variety of different voices. For Einstein, as for many creators, the language of intuition drew on visual and other forms of imagery. Kekule first discovered that the carbon atoms of the benzene molecule linked up into a ring through watching the flames of his fire transform themselves, in his mind's eye, into snakes that turned round and bit their own tails. Sometimes intuition emanates in an almost aesthetic judgement: what Nobel chemistry laureate Paul Berg calls 'taste'. 'There is another aspect I would add to intuition, and that is, I think, taste. Taste is almost the artistic sense. Certain individuals. . . in some undefinable way, can put together something which has a certain style, or a certain class, to it. A certain rightness to it.'

For others intuition manifests itself as a vague but trustworthy feeling of direction or evaluation - one 'just knows' which of several lines of enquiry to pursue, or which of a range of experimental results to take seriously, and which to ignore. Michael Brown (Nobel medicine laureate, 1985) describes how 'as we did our work, we felt at times that there was almost a hand guiding us. Because we would go from one step to the next, and somehow we would know which was the right way to go. And I really can't tell how we knew that. . .' While Stanley Cohen (Nobel medicine laureate, 1986), in similar vein, commented on the importance of developing a 'nose' for the important result - and of seeing this intuitive response as a valuable guide. 'To me it is a feeling of . . . "Well, I really don't believe this result", or "This is a trivial result" and "This is an important result" and "Let us follow this path". I am not always right, but I do have feelings about what is an important observation and what is probably trivial.' Note that Cohen acknowledges both the value and the fallibility of intuition. It can be wrong, and needs checking; but it none the less acts as source of guidance that is to be heeded and respected.

There are many accounts by creative artists and scientists of the need for patience and receptivity. In science, Konrad Lorenz, who won the Nobel Prize for medicine in 1973, stressed the importance of waiting. 'This apparatus. . . which intuits. . . plays in a very mysterious manner, because it sort of keeps all known facts afloat, waiting for them to fall in place, like a jigsaw puzzle. And if you press. . . if you try to permutate your knowledge, nothing comes of it. You must give a sort of mysterious pressure, and then rest, and suddenly BING, the solution comes.' While mathematician and philosopher George Spencer Brown declares, in his book Laws of Form:

To arrive at the simplest truth, as Newton knew and practised, requires years of contemplation. Not activity. Not reasoning. Not calculating. Not busy behaviour of any kind. Not reading. Not talking. Not making an effort. Not thinking. Simply bearing in mind what it is that one needs to know.

It is not, according to Lorenz and Spencer Brown, that one gives up on an intractable problem and drops it completely. The process is subtler than that. You do not try to figure it out, yet you 'give a sort of mysterious pressure’. You do not actively think, but you somehow 'bear the problem in mind'. It is as if you allow the problem to be there, to continue to exist on the edge of consciousness, yet without any purposeful attempt to bring it to a resolution. Nel Noddings, the American philosopher, describes this delicate balance of seeking and receiving in the more mundane context of studying a book.

The mind remains, or may remain, remarkably active, but instrumental striving is suspended. In such modes we do not try to impose order on the situation but rather we let order-that-is-there present itself to us. This is not to say, certainly, that purposes and goals play no role in our submitting ourselves to a receptive state. Clearly they do. We may sit down with our mathematics or literature because we want to achieve something - a grade, a degree, a job - but if we are fortunate and willing, the goal drops away, and we are captured by the object itself.

The gradual formation and development of an idea over a long time, perhaps from the tiniest of beginnings, and its delivery unwilled into consciousness, is a process that is as well known to artists as it is to scientists and mathematicians. Playwright Jean Cocteau both enthusiastically endorses the need to let the mind lie fallow, and attempts to scotch the idea that 'the muse' which springs from a patient state has anything magical or supernatural about it.

Often the public forms an idea of inspiration that is quite false, almost a religious notion. Alas! I do not believe that inspiration falls from heaven. I think it rather the result of a profound indolence and of our incapacity to put to work certain forces in us. These unknown forces work deep within us, with the aid of the elements of daily life, its scenes and its passions, and, when. . . the work that makes itself in us, and in spite of us, demands to be born, we can believe that this work comes to us from beyond and is offered us by the gods. The artist is more slumberous in order that he shall not work. . . The poet is at the disposal of his night. His role is humble, he must clean house and await its due visitation.

The historian John Livingston Lowe has made a detailed study of the sources and materials on which Coleridge based 'The Ancient Mariner', and has been able to trace in these sources the forgotten antecedents of every word and phrase that appears in the most vivid stanzas. He summarises the processes that must have been occurring, out of sight, in the poet's mind thus:

Facts which sank at intervals out of conscious recollection drew together beneath the surface through almost chemical affinities of common elements. . . And there in Coleridge's unconscious mind, while his consciousness was busy with the toothache, or Hartley's infant ills, or pleasant strollings with the Wordsworths between Nether Stowey and Alfoxden, or what is dreamt in this or that philosophy - there in the dark moved the phantasms of the fishes and animalculae and serpentine forms of his vicarious voyagings, thrusting out tentacles of association, and interweaving beyond disengagement.

Coleridge himself has described the composition of his other famous epic, ‘Kubla Khan’. Feeling slightly 'indisposed', as he puts it, he took some opium, and settled down to continue his reading of a work called 'Purchas's Pilgrimage'. Shortly he dozed off, just as he was reading, 'Here the Khan Kubla commanded a palace to be built, and a stately garden thereunto. And thus ten miles of fertile ground were enclosed with a wall.' Three hours later he awoke 'with the most vivid confidence that he could not have composed less than two to three hundred lines - if that indeed can be called composition in which all the images rose up before him. . . without any sensation or consciousness of effort.' Immediately Coleridge grabbed pen, ink and paper and 'eagerly wrote down the lines that are here preserved'.

American poet Amy Lowell describes how she uses incubation quite consciously as a trustworthy technique. 'An idea will come into my head for no apparent reason; "The Bronze Horses", for instance. I registered the horses as a good subject for a poem; and, having so registered them, I consciously thought no more about the matter. But what I had really done was to drop my subject into the subconscious, much as one drops a letter into the mailbox. Six months later, the words of the poem began to come into my head, the poem - to use my private vocabulary - was “there”.’

Incubation is a process that may last for months or years, but its value is not confined to such long periods of gestation. It works over days (as when we 'sleep on it', and find the problem clarified, or even resolved, in the morning), or such short spans as a few minutes. The French mathematician Henri Poincare, well known for his reflections on his own creative process, concluded:

Often when one works at a hard question, nothing good is accomplished at the first attack. Then one takes a rest, longer or shorter, and sits down anew to the work. During the first half-hour, as before, nothing is found, and then all of a sudden the decisive idea presents itself to the mind. . . The role of this unconscious work in mathematical invention appears to me incontestable, and traces of it would be found in other cases where it is less evident. . .       

There is now experimental evidence that corroborates these vivid anecdotes, and which helps us to understand how it is that incubation does its work. Steven Smith and colleagues at Texas A&M University have carried out a series of studies in which they were able to demonstrate incubation in the laboratory. Of course, they have not been able to reproduce the full complexity of the real-life creative experiences of an Einstein or a Coleridge. It is of the essence of such experiences that they cannot be directly manipulated or controlled. The undermind will not perform to order. Nevertheless, the results are informative.

The kinds of problems which Smith set his subjects were designed to mimic one of the key features of real-life creative insight: the discovery of a meaningful, but non-obvious, connection between different elements of the situation. So-called 'rebus' problems arrange words and images in such a way that they suggest an everyday phrase. For example:

ME      JUST   YOU

represents spatially the phrase 'just between me and you'. Or

TIMING         TIM ING

is a visual pun on the expression 'split second timing'.

Subjects were shown a succession of such puzzles, and initially given thirty seconds in which to attempt to solve each one. Some of the puzzles were accompanied by helpful 'clues' (such as 'precise' for the second example above), or unhelpful ones (such as 'beside' for the first one). Those problems that the subjects failed to solve the first time round were represented for a second try either immediately, or after a delay of five or fifteen minutes. When they had a second go immediately, subjects showed no improvement over their initial score. But when they were retested after a delay, performance improved by 30 per cent on the puzzles that had been accompanied by the unhelpful clues; and the longer (fifteen-minute) delay produced greater improvement than the shorter (five-minute) one. Significantly, the improvement did not depend on whether subjects had been able to work consciously on the problems during the delay, or had been given an irrelevant task to occupy their attention. So the benefit of incubation in this situation cannot be explained on the basis of having longer to think purposefully.

In another study, Smith elicited the incubation effect using the 'tip-of-the-tongue' (TOT) phenomenon, which occurs when you are trying to recall something - a name, typically - which just won't come to mind, though you have the strong feeling that it is 'on the tip of your tongue'. Using computer graphics, Smith invented pictures of imaginary animals, to which he attached names and a brief description of their supposed habits, habitats and diets. Subjects were given twelve such animals to study briefly, and then were asked to recall their names. As in the previous study, for the names they were unable to remember they were given a second recall test either immediately or after a five-minute delay. On this second test, they were asked to indicate, if they still could not get the name, what the first letter might be, if they thought they would recognise the name if they were shown it, and whether they felt that the name was on the tip of their tongue or not. The delay improved memory by between 17 per cent and 44 per cent And furthermore, even if subjects were unable to recall the whole name, their 'guesses' as to the first letter were more accurate when they said they were in the TOT state.

Smith suggests that in both studies there is a common explanation for the positive effect of incubation: the delay allows time for wrong guesses and blind alleys to be forgotten, so that when you come back to the task, you do so with a more open mind. There is a tendency to get fixated on a particular approach, even when it is patently not working. The delay increases the chances that your mind will stop barking up the wrong tree. 'When the thinker makes a false start, he slides insensibly into a groove and may not be able to escape at the moment. The incubation period allows time for an erroneous set to die out and leave the thinker free to take a fresh look at the problem.'

The idea that delay encourages a release from fixation, that it enables you to shake off unpromising approaches or assumptions that have been blocking progress, is certainly one aspect of incubation, but it cannot be the whole story, for it fails to take into account the active workings of unconscious intelligence. The fact that we can tell with a fair degree of accuracy when we are in the TOT state, whether we would be able to recognise the name if it were shown to us, and even, sometimes, retrieve its initial letter, or some other characteristic such as the number of syllables, suggests that the undermind has an idea what the word is, but for some reason is not yet willing or able to release that hypothesis fully into consciousness.

Yaniv and Meyer have shown directly that this sort of subliminal knowledge does exist. Like Smith, they investigated the TOT effect, this time reading to their subjects definitions of rare words and collecting those that subjects could not recall but felt sure they knew. They then used these words, along with other new words, in a 'lexical decision task', in which strings of letters were flashed on to a computer screen, and subjects had to press one of two keys to indicate, as quickly as they could, whether the string was a real word or not. It has been shown previously that words which have recently been seen, prior to the test, are recognised as being real words faster than other words which are equally familiar but which have not been recently 'activated' in memory. Yaniv and Meyer found that, even though the TOT words had not been consciously recalled, they still showed this 'priming' effect, indicating that they had been activated in memory, despite the fact that the 'strength' of the activation had not been great enough to exceed the threshold required for consciousness.

One of the effects of this partial activation is to increase the likelihood that some chance event may provide the extra little 'nudge' that is needed to get the word to tip over the threshold into consciousness - and this provides another way in which incubation can come about. Consciously you may think that you have made no progress towards the solution of the problem, and may even feel that you have given up. But unconsciously some progress might have been made; not enough to satisfy the criteria for consciousness, but enough to leave the 'candidate' somewhat primed. If some random daily occurrence serves to remind you, even if only subliminally, of the same word or concept, that may be sufficient to tip the scales, and you have the kind of sudden, out-of-the-blue experience of insight to which personal accounts of creativity often refer. Many people have had the experience of suddenly remembering a dream during the course of the day, when some trivial stimulus, such as a fragment of overheard conversation, acts as a sufficient nigger for: conscious recollection.

In the discussion of 'learning by osmosis', we saw that the undermind may be making progress in picking out a useful pattern of which the conscious mind is unaware. In such situations, we can show that we know more than we think we know. Does the same apply to the kinds of problem-solving that we are looking at in this chapter? Can we demonstrate directly that the undermind is closer to the solution of a problem than we think? And can we learn to be more sensitive to the subtle clues or indications that this is the case? Should we place greater trust, perhaps, in ideas that just pop into our minds, rather than treating them as random noise in the system, to be ignored? Recent studies by Kenneth Bowers and his colleagues at the University of Waterloo in Canada have suggested positive answers to these questions.

Like Smith, Bowers assumes that intuition is closely related to the ability to detect the underlying link or pattern that makes sense of seemingly disparate elements, and he has used both visual and verbal stimuli to explore the ways in which the undermind can home in on such patterns before conscious, deliberate thought has any idea what is going on. Consider the images shown in Figure.

One of each pair of pictures, either A or B, shows a highly degraded image of a real object. The other shows the same visual elements arranged in a different configuration. Subjects were shown a series of such pairs, and asked to write down the name of the object depicted in one of the drawings. If they were unable to do so, they were asked to guess which of the two images actually represented the real object, and to indicate their degree of confidence in this 'guess'. The results showed that people's guesses were better than chance, and that this was so even when they indicated that they had zero confidence in their guess. The possibility that the visual fragments of the real objects were somehow more coherently arranged, and that it was this perceptual clue, rather than any unconscious activity, that was informing the guesses, was discounted by showing the pairs of shapes to naive subjects and asking them to rate directly which looked the more 'coherent'. There was no difference in this judgement between the real and the rearranged images. Thus it appears, just as with the tip-of-the-tongue state, that the unconscious is able to indicate, in the form of what consciousness judges to be a complete guess, that it has got some way towards detecting the pattern, even when it has not yet been unequivocally identified.

The same finding is obtained with verbal rather than visual stimuli. Below are three pairs of three words. Within each pair, one of the sets of three words has a common (but not very obvious) associate-a single word that is related in some way to each of the three - while the other set of words is not connected in this way.

          A                  B

          STICK            PARTY

          LIGHT            ROUND

          BIRTHDAY      MARK

2        HOUSE           MAGIC

          LION             PLUSH

          BUTTER         FLOOR

3        WATER          SIXTEEN

          TOBACCO      SPIN

          LINE              TENDER

As with the pictures, people were asked to try to spot the connection, and if they could not, to indicate which of the two sets was the one that did have the (undetected) link. The results were essentially the same as with the visual stimuli: people were able, some of the time, to detect the presence of a pattern that they could not identify, and were able to do so more reliably than their own confidence ratings would suggest.

In an ingenious elaboration of this last study, Bowers devised what he called the 'accumulated clues task'. The problem was similar to the one just described: subjects had to discover the single word that formed the common associate to a number of other words. But now there was a list of fifteen such words, and they were presented in sequence, one at a time, rather than all together.

Accumulated Clues Test

1. RED

2. NUT

3. BOWL

4. FRESH

5. PUNCH

6. CUP

7. BASKET

8. JELLY

9. COCKTAIL

10. GUM

11. PIE

12. TREE

13. BAKED

14. SALAD

15. FLY

The first word was presented for ten seconds or so, during which time subjects were obliged to write down at least one association. Then the second cue word was revealed, and another response was required; and so on. When subjects thought that they had found a response that was a viable hunch or hypothesis, they marked it, but continued making further responses until they either changed their mind or were convinced that they had found the target word. Typically, over a number of such tests, people found a viable candidate on about the tenth word, and settled on a firm answer after receiving about twelve of the cue words.

If the unconscious can run ahead of consciousness, then people's 'guesses' might begin to converge on the target word before they realise it. In order to check this, the responses that subjects gave before they settled on a plausible hypothesis were presented to a panel of judges, to see if they bore any meaningful relationship to the as yet unidentified target word. Sure enough, they did. If they looked back over people's guesses, independent judges, who knew the solution, could see a pattern of steady approximation to the target; a pattern of which $e subjects themselves were unaware. It appears that the ideas that just pop into our heads may have greater validity than we think, and that we therefore deprive ourselves of useful information if we ignore them, or treat them as 'complete guesses'.

Bowers himself notes one important way in which these stylised problems are unrepresentative of problem-solving in real life. In the real world, a major part of the 'problem' is often that one does not know in advance what is relevant and what is not. The predicaments confronted by a business executive, an architect, a research scientist or a teacher are 'messy', in the sense that it is often not at all clear, at the beginning, how to conceptualise the problem, or what aspects of the available information to pay attention to and what to discard. The novice driver or medical student frequently feel overwhelmed with data because they have not yet discovered through experience what matters and what does not; what needs placing in the foreground of awareness and what can recede into the background. Bowers' puzzles, like many of those used by psychologists (and by those who design school curricula), are carefully tidied up before they are presented. The image of the camera is degraded, but there is no 'noise' in it. So in his most recent experiments, Bowers has made his problems more messy, and more lifelike. His tests now include some information that is irrelevant or distracting, as well as information that is relevant and valuable. Similar results seem to be emerging. For example, as they get closer (unbeknownst to them-selves) to a solution, so subjects get better at 'guessing' which of the details of the problem are actually relevant.

We now have empirical evidence for the existence of the mysterious 'guiding hand' that told Nobel laureate Michael Brown which step to take next, and Stanley Cohen which result to 'believe' and which to doubt. There is evidence, in other words, for the undermind, the intelligent unconscious that works quietly below, and in some cases ahead of, conscious apprehension. Both poets and scientists have always suspected as much. If they are observant, as they must be, they know it through their direct experience. When Amy Lowell was asked, 'How are poems made?', she replied: 'I don't know. It makes not the slightest difference that the question as asked refers solely to my own poems, for I know as little of how they are made as I do of anyone else's. What I do know about them is only a millionth part of what there must be to know. I meet them where they touch consciousness, and that is already a considerable distance along the road of evolution.’

While R. W. Gerard, writing in The Scientific Monthly in 1946, foreshadowed, with his acute speculations, much of what cognitive science is finally beginning to demonstrate beyond question.

Much attention has been given to the phenomena of learning: by the slow cumulation of a correct response in the course of experience ‘learning by osmosis’; and by the sudden grasp of a solution and abrupt performance of the correct response ‘intuition’. They seem very different. . . but it is possible, perhaps probable, that they are basically quite similar. In both cases, new functional connections must be established in the brain; and this process may be more gradual and cumulative in the case of 'insight' than it appears. For here, also, much brain work precedes the imaginative flash - the theory of gravitation may result only when the metaphorical apple falls on the prepared mind - and only when the process has progressed to some threshold level does it overflow into a conscious insight.”