CREATIVITY: INSPIRATION, INTUITION OR ILLUSION? CSRP 322 Margaret A. Boden School of Cognitive and Computing Sciences 亚洲情色 [To be published as the 1994 Templeton Lecture, Centre for Human Aspects of Science and Technology, University of Sydney: as a pamphlet, and later by Scottish Academic Press.] I: INTRODUCTION The Gilbert islanders of the Pacific build a "maneaba", or sacred meeting house, on the western shore of their inhabited islands [Maude, 1980]. It has a large thatched roof of pandanus wood and leaves, set not on walls but on several pillars of coral. One long side faces the lagoon, or ocean, to the west. The idea of the maneaba was created long ago, far back in Gilbertese history, and has been faithfully celebrated -- and implemented -- ever since. The placement, planning, and construction of the building are highly ritualized. It must have one of nine different sets of proportions. The trees must be felled with an adze made from a clam shell, and the proportions measured by human body-parts or by fronds cut from a coconut palm. A series of magical poems, sung by the builders while they work, remind them how to use coconut-fibre strings in marking out the site, and when and where to place the foundation- posts, roof-rafters, and so on. Every detail is specified by Gilbertese tradition. The finished building is rectangular -- for practical purposes, perfectly so. But meticulous measurement will always show the rectangle to be imperceptibly skewed. And the central ridge-pole is always slightly off-centre. "Hardly surprising!", you may say. "How could such primitive technology be expected to do any better? After all, a perfectly rectangular black slab was used by Arthur Clarke, in "2001, A Space Odyssey" as an unmistakable sign of superior power. Rectangularity is difficult to achieve." Well, you might be right about the difficulty. But you would be wrong about the "primitive technology". The breadth, width, and height of the maneaba are all accurately measured, and their traditional proportions ensured, using the strings and fronds of the coconut palm. (The chants and ritual movements take the place of Euclidean geometry.) The skew in the rectangle arises because the roof-plate on the eastern side is carefully made very slightly longer than that on the western side. Moreover, at an early stage of the building process the ridge-pole is absolutely central, its supporting poles being precisely positioned on the mid-line. However, this perfection is then deliberately ruined, by pushing the tops of the supporting poles a hand's breadth to the west. These "deliberate mistakes" in the construction are introduced so as not to tempt the malevolent spirits in the west. (Their mythical malevolence is historically grounded: the ancestors of the maneaba- builders came from Samoa, in the east, and chased the original islanders further westwards.) The precise nature of the imperfections, such as the greater length of the eastern side, symbolize the superiority of the newcomer-islanders' power over that of the original inhabitants -- and of evil influences in general. This example is a reminder of two important aspects of our usual response to creativity. First, is the sense that the products of human ingenuity can point beyond themselves and their immediate function, calling up other aspects of our experience -- sometimes, aspects touching our deepest feelings. Second, is the sense that a perfect man- made product (an artefact or an idea) may be close to the superhuman. Arthur Clarke assumed both these responses in his fictional characters, and expected them of his readers too. The ancient Greeks felt that human attempts at perfection smacked of hubris, inviting retribution from the gods. As for the Gilbert islanders, they value perfect rectangularity -- but not quite as much as safety from revengeful spirits. In short, a common human response to perfection (or even near-perfection) in created works is a sense of wonder, which reaches deep into our experience -- and points, perhaps, beyond the purely human. Westerners, being less communal and ritualized than the Gilbertese, are interested in creativity in individuals. What they have said about it shows that creativity can seem abnormal, superhuman, perhaps even divine. Indeed, reflecting on creativity often leads Westerners to, or confirms them in, a hostility to Western science. At the very least, it seems to throw doubt on the possibility of a scientific psychology of creativity. Some of these people hold that human creativity is not human at all, but divine. Plato said "A poet is holy, and never able to compose until he has become inspired, ... for not by art does he utter these [words], but by power divine". Two millennia later, the essayist Bernard Levin wrote in the London Times that Mozart was (literally) divinely inspired. The perfection of his music, the mismatch between his music and his life, and his own ignorance of the sources of his compositions were each cited by Levin as reasons for attributing Mozart's musicianship to God, not to Man. Others hold that creativity, while not actually superhuman, is a special power or gift, perhaps limited to a human elite. On this romantic view, creativity involves intuition. By "intuition", here, is meant a mysterious faculty unlike any other, which gives us (or some of us) the power to come up with new ideas. Logic, normally the scourge of mystery, adds to the mystery here. If a new idea really is new, really is radically different from what went before, how could it possibly be explained in terms of its psychological predecessors? The very idea seems paradoxical. The same logical point has surfaced in metaphysics and theology. How is it conceivable, for instance, that a purely immaterial God could create a material universe? This logico-theological conundrum has led to the "emanations" of the neo-Platonists, the Christ "begotten, not created" of the Nicene creed, and the all-encompassing pantheism -- or, on another interpretation, the uncompromising atheism -- of Spinoza. Logic, then, seems to dismiss creativity as an illusion. And where logic goes, science must follow -- for, surely, there can be no scientific explanation of fundamental novelty? Moreover, there is clearly no possibility of explaining creativity in scientific terms if inspiration is the key. The same is often said by those who think of intuition as the source of our creative powers. For intuition (as defined above) is a romantic's faculty, posited specifically to distance creativity from other mental powers, and to preclude any scientific explanation of it. In short, creativity sets a problem for logic, for theology, and for science. Many tough-minded individuals sidestep the logic, ignore the theology, and briskly favour the science. They argue that there is nothing particularly problematic about human creativity: a creative idea is merely a novel (and valuable) combination of familiar ideas. As such, it could in principle be explained in scientific terms, by psychological theories that explain how such novel combinations can come about. Up to a point, they are right. Samuel Taylor Coleridge's questions about "the hooks and eyes of memory", for instance, could be answered by scientific theories about the associative processes in the poet's mind (or brain). Indeed, current computer models of so-called neural nets provide some preliminary ideas about just how such mental associations could happen. Using those ideas, we can lay scientific foundations for the "Road to Xanadu" described in a fascinating literary study of the sources of Coleridge's poetic imagery [Boden, 1990, ch. 6; Livingston Lowes, 1951]. And theories (and computer models) of analogy suggest how two ideas can be seen as analogous, being matched in various ways according to the context of thought [Boden, 1990, ch. 7; Hofstadter et al. in press]. That's not to say that we already understand all aspects of analogy, or of association, for we do not. However, psychology can reasonably hope to explain many examples of creativity in such terms. But is that enough? Could science explain all creativity by reference to novel combinations? If not, could it explain other cases in other terms? And, in the event of a successful scientific explanation, what follows? Would it show creativity to be an illusion? And does science destroy wonder? Does it threaten to undermine our joy and awe in the face of creative ideas? -- These questions are my topic, here. II: Exploring and Transforming Conceptual Spaces Creative "ideas" include scientific theories; musical compositions; literary genres; instances of choreography, painting, and architecture; theorems of mathematics; and the inventions of engineers. As already remarked, some of these can be understood as mere novel combinations of familiar ideas. But many cannot -- especially those which not only solve the creator's initial problem but also engender a whole new set of problems, to be solved perhaps by the creator's successors over many years. Exploring the implications of a radical new scientific theory, or of a new poetic or musical genre, is not a matter of mere combination- juggling. On the contrary, it is a structured, disciplined, sometimes even systematic search for the meanings promised by the new idea. But how can this be? How can a new idea be pregnant with such promise? Imagine a traveller, perhaps a character in one of Rider Haggard's novels, trekking through a desert and up a barren mountainside -- only to see, from the crest of the hill, a verdant valley stretched out before him. The promise, the possibilities, are enormous. But to find them, he will have to explore the valley -- sketchily at first, perhaps, but later seeking treasures in many a nook and cranny. Creative thinkers (which means all of us, on a good day) explore the possibilities inherent in their own minds, wherein the spaces are not geographical but conceptual. A conceptual space is a style of thinking, a mental skill that may be expressed in marble, music, or movement, in poetry, prose, or proof [Boden, 1990, esp. ch. 4]. It is defined by a set of constraints (the dimensions of the space) guiding the generation of ideas in the relevant domain. Some of these constraints are accepted, by the thinker and by the relevant social group, as being more inescapable than others. And some -- as we shall see -- are more fundamental than others. Together, they form a mental landscape with a characteristic structure and potential. Think of the disciplined beauty of a Palladian villa, for instance, or the clean lines of a Frank Lloyd Wright open-plan "Prairie House". Or think of the structure of modern atomic theory, or of Mendeleev's periodic table of the elements (which in 1859 had several empty spaces in it, to be explored by chemists later). Or again, think of the stylistic differences between blank verse, a sonnet, and a limerick, or between the cadences of Coleridge's "Rime of the Ancient Mariner" and those of Longfellow's "Hiawatha". The common notion that creativity is unconstrained is mistaken: constraints make creativity possible. Without them, thought would be mere unstructured chaos -- or, at best, a succession of fleeting mental combinations, individually fascinating but stylistically unproductive. They are not negative constraints ("thou shalt nots") so much as positive ones, guiding the thinker to desired ideas, fruitful pathways, and valued corners of the conceptual space. However, they are not cast in stone -- which is partly why people so often describe creativity as unconstrained. (Another reason is that creativity is unpredictable in various ways [Boden, 1990, ch. 9].) The thinker has one great advantage over Rider Haggard's hero, quite apart from the fact that his exploration is (usually) less physically dangerous. For as well as exploring his mental landscape, he can also change it. Many highly valued, and historically celebrated, creative ideas are cases where the conceptual space concerned has been transformed, at a relatively fundamental level. Either a new constraint (a new dimension, helping define a new conceptual space) has been added, or one of the previously accepted constraints has been altered: weakened, strengthened, dropped, negated, repeated, inverted, varied (by substituting different numbers, colours, or chemical elements) ... and so on. Exploratory creativity is not to be sneezed at. Many creative people earn fortune, and even fame, from exploring a given style. Exploration enables someone to get a sense of the structure, potential, and limits of a space before transforming it in some appropriate way. And it can throw up unexpected treasures. Mozart was not a great transformer, not an adventurous musician (like Haydn); his greatness lay rather in his sustained capacity to explore and exploit the unrealized (and unexpected) potential of pre-existing musical spaces. Similarly, the rich possibilities of the Palladian villa were explored by Palladio, and by architects after him, with good effect. And most scientists work within a theoretical space, rather than transforming it. It is not always clear where exploration ends and transformation begins: a space may be "tweaked" in many ways without being fundamentally transformed. Imagine a neo-Palladian villa with semi- circular window-bays: since no window-bays, and virtually no curves, occur in Palladio's own work, this architectural exploration has changed the space, to some degree. The Palladian inspiration remains obvious, however: here, we have tweaking rather than transformation. By contrast, the deepest creative surprises result from fundamental change in the thought-space. Think of the history of post-Renaissance Western music, for example. The evolution of the well-tempered scales from the mediaeval modes defined a harmonic space which was gradually explored by composers, who introduced increasingly many -- and increasingly daring -- modulations, leading the piece temporarily out of the home key. Eventually, someone (it happened to be Schoenberg) dropped the fundamental constraint of the home key, and in so doing moved out of tonality into atonal music [Rosen, 1976]. Or think of the nineteenth- century chemist Kekule's achievement in thinking of the benzene molecule as a closed ring, not (as previously assumed) an open string. In doing this, he not only described the structure of benzene. He also generated the space of aromatic chemistry (which, when explored, told us about the many benzene derivatives), as well as making possible other areas of chemistry dealing with other ring-molecules (based on fewer than six atom, or on elements other than carbon). The new space is closely related to the old one from which it sprang -- were this not so, the new ideas would be unintelligible. The more fundamental the change in the relevant constraints, the more difficult it is to understand, and so to value, the new creation. Sometimes, it takes most people many years to appreciate it, and then only if they spend time in exploring both the old and the new spaces, so as to get a sense of the dimensions which they have in common, as well as those in which they differ. This is true both in science and in art, although science has the advantage that valuation rests largely (but not entirely [Schaffer, 1994]) on objective data and repeatable experiment. To transform a space is to make certain ideas thinkable which previously were unthinkable. The shock of surprise one experiences on first confronting such an idea is grounded in one's appreciation that, relative to the space in its earlier form, it was impossible. Combination-theories cannot capture this sort of surprise, for they deal with mere statistical improbability. A Schoenberg, or a Kekule, seem to offer us not an improbability but a satisfying, and potentially productive, impossibility. To be sure, this "impossibility" happened. That is, it was not impossible relative to the total resources of the thinker's mind -- which include various ways (some mentioned above) of transforming conceptual spaces. III: Mechanisms of Creativity You may agree with everything I've said so far, yet doubt whether science could define conceptual spaces, still less explain how we explore and transform them. Surely, these are matters for the traditional humanities -- and for wonder, not scientific explanation? Science as such does not define conceptual spaces. That is the job of the literary critic, the musicologist, and the historian of art or science. But science can help. In particular, it can indicate where the humanities' current definition is silent or unclear, and where it is right -- or wrong -- in ascribing a specific generative range to the conceptual space concerned. Consequently, it can lead us to features of creative domains which more traditional scholarship has missed. Moreover, science can help us understand the psychology of exploration, and (up to a point) transformation. It does this by way of computer modelling, using the techniques of artificial intelligence (AI) and computational psychology. AI-workers try to get computers to produce performance like that of a human being, but they may not care whether the computer does it in a very different way. Computational psychologists, by contrast, are primarily interested in human minds. They use concepts drawn from AI in formulating theories about mental processes, and they test their theories in the form of computer models. We have already noted, in Section I, that connectionist computer models (neural networks) can help to explain combinational creativity, such as literary imagery or scientific analogy. Here, the point of interest is that computational concepts can help us also to define conceptual spaces clearly -- and to explore and (sometimes) transform them, too. In short, they can help us to understand how creativity is possible [Boden, 1990]. Let's consider two examples mentioned earlier: the Palladian villa and the Prairie House. Even the ritualized Gilbertese maneaba is allowed nine different sets of proportions, as we have seen. But these Western building-styles, developed within a culture that values individuality more highly, appear in many more than nine allowable forms. Frank Lloyd Wright designed about forty Prairie Houses, most of them unique despite their recognizable style. And Palladian villas abound: new examples are still being built, centuries after Palladio's death. A leading expert on the architecture of Frank Lloyd Wright, having devoted an entire chapter to the Prairie Houses, declared their (intuitively evident) architectural balance to be "occult" [cited in Koning & Eizenberg, 1981, p. 322]. We are presumably meant to infer that the stylistic unity of these houses is a mystery accessible only to aesthetic intuition, and that only the peculiar genius of Frank Lloyd Wright could have designed them. However, to say that a style is recognized intuitively does not mean that some power or faculty of intuition enables us to recognize it. Rather, it means that we are unable to say, explicitly, how we do so. There is nothing unusual in this. Perhaps you can distinguish traditional and modern jazz, or grammatical and ungrammatical sentences -- but can you say just how they differ? As regards the explanation of creativity, "intuition" is the name of a question, not of an answer. Moreover, it is a question that can sometimes be answered. A computationally inspired study of the Prairie Houses has defined an architectural "grammar" of 3D-shapes that generates the examples designed by Lloyd Wright, as well as new houses which -- to the intuitive (educated) eye -- obviously fall within the same style [Koning & Eizenberg, 1981]. The basic 3D-shapes are cuboids, so are rectangular in plan; but because they can be added to each other "sideways on", the overall house-plan is not rectangular. (The grammar is a paper-and- pencil rule-following exercise, but it can be expressed as a computer program.) The conceptual dimensions of the Prairie House space (the rules of the architectural grammar) are clearly identified as more or less fundamental. Decisions about the existence, number, and nature of balconies are made very late, so cannot affect the design of the house as a whole. Accordingly, added balconies are seen as stylistically (as well as literally) superficial. By contrast, decisions about the fireplace (or fireplaces) must be made very early, other design- decisions depending on them. Consequently, to "add" a fireplace is to make a fundamental alteration to the overall structure of the building. If the grammar is followed, however, it will still be recognizable as a form of Prairie House. Since the grammar allows a range of choices at each choice-point, one can move into various regions of the conceptual space, differing from neighbouring regions in more or less fundamental ways. Distinct "families" of houses inhabit different regions of the space, and our intuitive sense of similarity and dissimilarity can be specified accordingly. The principle of unity is no longer occult, but has been made explicit. The grammar could help us not only to explore the architectural space, but also to transform it. If one or more grammatical rules (conceptual dimensions) were to be changed, then the relevant conceptual space would be transformed -- and the more fundamental the rule, the deeper the transformation in the style-space. The designs found when exploring this space would be aesthetically related to the Prairie style, but also different from it. Someone who knew the two grammars concerned would be able to specify the architectural differences precisely. Someone to whom the grammars were hidden (occult) might be able to recognize that the most recent designs differ (subtly or fundamentally) from Prairie Houses, without being able to state the difference clearly. All these points could be made about other styles of architecture [Mitchell, 1990]. For the Palladian villa, they have been made in great detail. The rules of Palladian thought-space have been expressed as a shape-grammar (for generating architectural plans) [Stiny & Mitchell, 1978], and as a computer program that considers dimension and proportion as well as shape, and generates facades as well as plans [Hersey & Freedman, 1992]. Given our discussion of conceptual spaces as sets of possibilities, and of transformations as enabling ideas that were previously impossible, it's worth noting that "the book of the program" is called "Possible Palladian Villas (Plus a Few Instructively Impossible Ones"). Like the Gilbertese maneaba, the Palladian villa has a rectangular outline, and preferred numerical proportions and dimensions. Unlike a maneaba, it has walls -- including internal walls, which divide the plan into smaller rectangles. However, not any rectangles will do: the rooms are positioned and proportioned with a care reminiscent of the Gilbert Islanders, but by means of mathematics and geometry instead of chants and palm-fronds. Palladio designed many variations on his basic rectangular theme, which survive as actual buildings or as drawings. He also left some remarks describing his design-technique, such as his habit of "splitting" rectangles vertically or horizontally. But art-historians have long disagreed about just what are the underlying rules. The Palladian program is an attempt to clarify them. Its success must be judged on three criteria. First, is its ability to generate, or closely approximate, designs ACTUALLY PRODUCED by Palladio. Second, is its ability to come up with new designs recognizable as Palladian, which he MIGHT HAVE thought of, but didn't. And third, is its ability to avoid non-Palladian designs, structures which Palladio WOULD NOT have produced. The last two criteria require aesthetic judgment as well as historical evidence, and in that sense are subjective. However, many such judgments are non-contentious. Some unarguably non-Palladian features occur in houses built by his imitators, and others were produced by early versions of the program. These include bays (even rectangular ones) jutting out from the rectangular perimeter; internal corridors; long, thin rooms; too many rooms; rooms of greatly disparate size; many internal (windowless) rooms; and the largest room's lying off the central axis. Other "departures" are more debatable. For instance, Palladio almost never built cylindrical rooms, and only rarely abandoned mirror- image symmetry (by adding an extension on only one side). Should we say that an architect (or program) who does so is faithful to Palladio's inspiration, or not? When does tweaking amount to transformation? Whatever our answer, the grounds of judgement have been made explicit. So there is more chance of fruitful debate, and even of agreement. This work can help to show whether, on a particular occasion, Palladio was exploring, transforming, or simply ignoring his own creative constraints (and, sometimes, his own advice on architectural design). It can also indicate how far a building designed by someone else is, or is not, in the Palladian style. The authors point out, for instance, that the "Palladian" Lord Burlington often included features (including rectangular bays) very different from what Palladio would have allowed. Accordingly, many disputes about Palladio's oeuvre have been clarified or even settled. Does this work count as psychology? Certainly, scientific explanation was not the researchers' main concern. Nor were they aiming to outdo James Gibbs or Lord Burlington, in designing new Palladian villas (a perfectly reasonable ambition). "Rather," they say, "knowing what Palladio would and would not do deepens our understanding of what he actually did do" [Hersey & Freedman, p. 10]. A clearer statement of the use of computer modelling for the scholarly and aesthetic interests of the humanities, it would be hard to find. However, psychologists hoping to explain (for instance) how architects create new designs need to know which constraints they consider, and in what order. Only then can they fruitfully ask what sorts of mental process might explain the activity. The Palladian program is therefore relevant for psychologists interested in creativity. You may feel that classical, and much modern, architecture is relatively easy to discuss in computational terms. After all, the aesthetics of the Palladian style have always been described in terms of mathematical regularity and proportion, and Lloyd Wright presented his Prairie Houses as examples of a single, minimalist, architectural paradigm. Perhaps we should consider something more spontaneous, less "cut and dried"? What about jazz improvisation? This is normally regarded as one of the peaks of spontaneous creativity, and to many people appears less constrained than even the most undisciplined architecture. The former view is justified, but the latter is not. The conceptual space of jazz improvisation has been partially mapped by two programs, each of which was written in an attempt to understand how the human musician does it. One is a program designed to teach people to improvise jazz [Hodgson, 1990; Waugh, 1992]. It clearly defines various dimensions of the musical space, and various ways of travelling through it. The program can be left to wander through the space by itself, in which case it will improvise -- on a given melody, harmony, and rhythm -- by making (random) choices on many dimensions simultaneously. Quite often, when it is working in this fashion, it creates novel musical ideas which a professional jazz-musician finds interesting, and may wish to develop in his own playing. Alternatively, the human user can make the program concentrate on one (or more) dimension at a time and explore it (or them) in a very simple way. This is why it can help jazz-novices, who can focus on the aspect of jazz that is currently causing them difficulty. Many dimensions of musical space are explored by this jazz- improviser (and other exploratory pathways are at present being added [Hodgson, in preparation]). For instance, the program can produce fragments (of random length) of ascending or descending scales, ensuring that the scale chosen is the one relevant to the harmony at that particular point. It can provide "call" and "reply" over two or more bars. It can replace the current melody-note by another note drawn from the same scale, or provide a chromatic run between this melody-note and the next. It can "cut and paste" a library of melodic and rhythmic patterns, or play fractionally ahead of or behind the beat. And it, and the human user, can vary the frequency with which it does any of these things. Because the thematic melody, harmony, and metre -- and the library of musical patterns -- are all provided to this program at the start, it is not limited to jazz. It can cope with other forms of tonal music. Give it "seeds" from Bach or Mozart, or a Latin American bossa nuova, and it will improvise accordingly. In a sense, that is a strength. But it is also a weakness, for the program cannot compose its own seeds. Not only is it incapable of constructing a "Bach invention" or "Debussy prelude": it cannot compose a jazz theme, either. However, another program can do so, not only improvising an acceptable melody but composing the basic chord sequence, too [Johnson-Laird, 1991]. (For the record, yet another program, which can imitate Bach or Debussy, or any other Western or non-Western composer, does not do so "from scratch": it starts by analyzing a data-base of music written by the composer it is imitating [Cope, 1991].) The second jazz-program, because it does start from scratch, has an even more challenging task. (Or rather, its programmer does.) It plays merely at the level of a moderately competent beginner, whereas the first can sound like an average professional jazz-musician. But it tells us even more about the conceptual space concerned, and suggests some specific ways in which human musicians move through it. For instance, it distinguishes creative journeys that can be made very quickly, and journeys that take more time. Human short-term memory is very limited, yet good jazz-musicians can improvise as fast as they can play. This implies that the rules they use for improvisation put very little load on their memory. Accordingly, when this program improvises the melody, harmony, meter, chord, and passing notes (all of which must be mutually consistent), it never looks back beyond the immediately preceding note or chord. By contrast, people cannot compose chord sequences very fast (they are agreed before the improvisation starts). The reason is that jazz chord sequences can have a complex, hierarchically nested, structure -- rather like sentences. A simple chord sequence may be comparable to "The dress is purple", but interesting ones are more like "The dress that the girl the cat the dog bit last Saturday scratched sewed is a very deep shade of purple". This last sentence does not trip easily off the tongue: it takes some time (and thought) to produce. The program that generates jazz from scratch is therefore made up of two parts. One composes complex chord sequences, using significant time and memory to do so. Its output is then fed as input to the other part, which improvises on it in real time, using rules requiring very little memory. In jazz as in architecture, then, a computational psychology can help us understand what goes on in creative minds. Science can help humanist scholars to define the conceptual spaces concerned, and it can tell us something about how, in practice, they can be explored. But what about transformations? None of the programs I've mentioned transforms one style into another -- although one of them can "mix" styles, by mixing data-bases (of Bach and Scott Joplin, for example) [Cope, 1991]. Perhaps it is in principle impossible for a computer model to transform its way of working? Well, no. Transformations, even for computer programs, are relatively easy. The difficulty lies in selecting those most likely to be fruitful and interesting, as opposed to boring or even destructive. Sometimes, this evaluation is done by the human user. Sometimes, however, it can be left to the computer itself. The most intriguing examples, here, are programs using "genetic algorithms" (GAs). GAs are rules that enable a program to change some of its own rules, and they are modelled on the genetic changes (mutation and crossover) underlying biological evolution. Random changes to the rules specifying the program's way of doing what it does (problem-solving, image-drawing, or whatever) are repeated for many generations, the "best" instances at each generation being selected to act as the parents of the next. The selection is sometimes done automatically, by the program itself. Clearly, this can happen only if the program's task is one for which relative "success" can be clearly defined by the programmers. Even so, the program's style of tackling the task may evolve in an utterly unexpected way. For example, a program that designs very simple robot "brains" may eventually create a design in which redundant sensory or motor "organs" (such as un-needed whiskers, or an extra, unnecessary, eye) are de-inervated, the relevant "brain-cells" being taken over for other purposes [Cliff, Harvey, & Husbands, 1993]. In other cases, the evaluation at each generation is done by the human user. This is true of two evolutionary programs whose task is to generate coloured images. There is an interesting difference between them, one which reminds us of the discipline essential to creativity. The first graphics-program explores highly complex 3D-shapes, with many buds, folds, and whirls [Todd & Latham, 1992]. One of the authors, a professional artist and trained sculptor, chooses the most aesthetically interesting shape at each generation, and the program then mutates it randomly to produce the next set of siblings. I said the program "explores" its conceptual space because, although it produces designs the human artist would not have thought of, there is an obvious family likeness between the descendants -- especially those separated by only a few generations. The program can generate images in distinct styles, but these have to be differentially seeded by the programmer. Having been given a style, the program may push towards its boundaries but can never surpass them. It is as though Palladio's villas could be varied and evolved by a host of admiring imitators, but could never result in the shocking novelty of a Prairie House. The reason is that the program's GAs are allowed to touch only relatively superficial aspects of the code, such as numbers. A piece of "whirly" code can mutate into very-whirly code, but it cannot suddenly change into a rectangle-generator. In other words, tweaking is all this program can achieve, even though the final image may (after many generations) look like a transformation of the first. There is nothing comparable to Schoenberg's or Kekule's sudden changes to fundamental constraints of music or chemistry. Sudden transformations are seen, however, in the second graphics- program [Sims, 1991]. Here, the GAs can get down into the heart of the image-drawing code, and change its fundamental structure. For instance, they can conjoin one piece of code with another, or nest one hierarchical structure inside another. Consequently, the "offspring" of a given image or pair of images can be very different indeed from their parents. They can have such different colours and shapes that even the programmer cannot tell us just how they were created from the previous generation (and this is true even though he can get a print-out of the altered code). To be sure, there is usually some faint similarity. But tonal and atonal music, or aromatic and nonaromatic chemistry, are similar too. Transformation does not destroy similarity entirely. But it does produce deeply surprising results, by making ideas possible which were unimaginable before. One must beware, however, of saying that the second graphics- program is "more creative" than the first, or more relevant to studies of human creativity. It's no accident that it is the professional artist who has chosen not to allow his program's GAs to alter the heart of its code. He (like Palladio) is interested in a disciplined exploration of a certain aesthetic space. If someone were to change his program overnight to enable it to transform its code, he would either discard the resulting images as "uninteresting", or choose one and then explore (and tweak) that in a relatively systematic way. Only when he feels that the aesthetic potential of the relevant style-space has been fairly fully explored will he spontaneously move into another one. A convincing computer model of creative transformation would have to be able to tweak, too. It would have to evaluate its transformations so as to decide which to follow up (explore) and which to discard. And it would need to sense when a style had been fully explored, and when it might have hidden regions not yet entered. In addition, it would need to change its principles of evaluation, as its creative powers evolved. None of this is in principle impossible. But its possibility is relevant here for only one reason: our concern is not with computers as such, but with how they can help psychologists learn about human minds. The examples discussed above suggest that we are on the way towards a scientific understanding of creativity. IV: Science and Wonder Inspiration, intuition, or illusion: creativity is none of these. People often fear that science must dismiss creativity as an illusion. Creative ideas are among the most awe-inspiring achievements of humankind. If they are illusory, so much the worse for Mozart, for Palladio ... and for us. Fortunately, this fear is unfounded. A scientific psychology does not deny creativity, in suggesting what mental processes could make it possible. Nevertheless, you may feel subtly cheated. There is at least this to be said for unscientific talk of "inspiration" or "intuition", that it presents creativity as something precious, something to be wondered at. Any scientific account, you may feel, must demystify creativity -- and, in so doing, devalue it. But science itself springs from an awed appreciation of the hidden mysteries of the natural world, and from the human desire to understand them. Understanding need not drive out wonder. Sometimes, of course, it does. When our wonder is based (for example) on a sentimental over- estimation of a creature's mental powers, science may demystify with a vengeance. The "parental foresight" and "maternal care" of a female dove look less estimable when ethologists explain that the bird produces a series of (adaptively appropriate) behaviours, each independently triggered by some hormonal or environmental cue [Lehrman, 1955, 1958a, 1958b]. But a human mother's parental behaviour is a very different matter. Only if it were shown to be just as unthinking as the dove's would we be forced to withdraw our respect and admiration for her unselfish care and planning. Similarly for creativity. It is not LESS complex, subtle, and admirable than we had assumed, but more so. In indicating how it is possible, science has confirmed (what Coleridge claimed) that even novel combinations draw on associative mental processes that are far from simple; they can be highly idiosyncratic, and they allow for serendipity [Boden, 1990, ch. 9]. Also, science helps us to understand the richness and creative potential of conceptual spaces, and the processes by which we explore and transform them. These psychological factors underlie the generation, and the recognition, of creative ideas. The ideas themselves remain, for our delight. Palladian architecture, or jazz, is no less wonderful for being better understood. We can share the Gilbert islanders' awed response to rectangular perfection, if not their mythological reasons for avoiding it. REFERENCES Boden, M. A. [1990] The Creative Mind: Mayths and Mechanisms London: Weidenfeld & Nicolson. (Now published in the UK by Oxford University Press, and Abacus paperbacks.) Cliff, D., I. Harvey, & P. Husbands. [1993] "Explorations in Evolutionary Robotics". Adaptive Behavior 2, 73-110. Cope, D. [1991] Computers and musical Style Oxford: Oxford University Press. Hersey, G., & R. Freedman. 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