Hare Brain, Tortoise Mind

by Guy Claxton

  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 arc, 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.’6 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.7 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.8

  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’.9 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. (Emphasis added)

  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.’10

  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 cr
eators, the language of intuition drew on visual and other forms of imagery. Kekuté 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.11

  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.12 (Emphasis added)

  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.13 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.14

  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’.15

  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 Poincaré, 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 re-presented 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.