Читать книгу The Creativity Code - Marcus du Sautoy - Страница 7

The chief enemy of creativity is good sense.

Pablo Picasso

The value placed on creativity in modern times has led to a range of writers and thinkers trying to articulate what it is, how to stimulate it, and why it is important. It was while sitting on a committee at the Royal Society assessing what impact machine learning was likely to have on society in the coming decades that I first encountered the theories of the cognitive scientist Margaret Boden. Her ideas on creativity struck me as the most relevant when it came to addressing or evaluating creativity in machines.

Boden is an original thinker who over the decades has managed to fuse many different disciplines: philosopher, psychologist, physician, AI expert and cognitive scientist. In her eighties now, with white hair flying like sparks and an ever-active brain, she is enjoying engaging enthusiastically with the prospect of what these ‘tin cans’, as she likes to call computers, might be capable of. To this end, she has identified three different types of human creativity.

Exploratory creativity involves taking what is already there and exploring its outer edges, extending the limits of what is possible while remaining bound by the rules. Bach’s music is the culmination of a journey Baroque composers embarked on to explore tonality by weaving together different voices. His preludes and fugues push the boundaries of what is possible before breaking the genre open and entering the Classical era of Mozart and Beethoven. Renoir and Pissarro reconceived how we could visualise nature and the world around us, but it was Claude Monet who really pushed the boundaries, painting his water lilies over and over until his flecks of colour dissolved into a new form of abstraction.

Mathematics revels in this type of creativity. The classification of finite simple groups is a tour de force of exploratory creativity. Starting from the simple definition of a group of symmetries – a structure defined by four simple axioms – mathematicians spent 150 years producing a list of every conceivable element of symmetry, culminating in the discovery of the Monster Symmetry Group, which has more symmetries than there are atoms in the Earth and yet fits into no pattern of other groups. This form of mathematical creativity involves pushing the limits while adhering to the rules of the game. It is like the explorer who thrusts into the unknown but is still bound by the limits of our planet.

Boden believes that exploration accounts for 97 per cent of human creativity. This is the sort of creativity that computers excel at: pushing a pattern or set of rules to the extremes is perfect for a computational mechanism that can perform many more calculations than the human brain. But is it enough? When we think of truly original creative acts, we generally imagine something more utterly unexpected.

The second sort of creativity involves combination. Think of how an artist might take two completely different constructs and seek to combine them. Often the rules governing one world will suggest an interesting new framework for the other. Combination is a very powerful tool in the realm of mathematical creativity. The eventual solution of the Poincaré Conjecture, which describes the possible shapes of our universe, was arrived at by applying very different tools to understand flow over surfaces. It was the creative genius of Grigori Perelman which realised that the way a liquid flows over a surface could unexpectedly help to classify the possible surfaces that might exist.

My own research takes tools from number theory to understand primes and applies them to classify possible symmetries. The symmetries of geometric objects at first sight don’t look anything like numbers. But applying the language that has helped us to navigate the mysteries of the primes and replacing primes by symmetrical objects has revealed surprising new insights into the theory of symmetry.

The arts have also benefited greatly from this form of cross-fertilisation. Philip Glass took ideas he learned from working with Ravi Shankar and used them to create the additive process that is at the heart of his minimalist music. Zaha Hadid combined her knowledge of architecture with her love of the pure forms of the Russian painter Kasimir Malevich to create a unique style of curvaceous buildings. In cooking, too, creative master chefs have fused cuisines from opposite ends of the globe.

There are interesting hints that this sort of creativity might also be perfect for the world of AI. Take an algorithm that plays the blues and combine it with the music of Boulez and you will end up with a strange hybrid composition that might just create a new sound world. Of course, it could also be a dismal cacophony. The coder needs to find two genres that can be fused algorithmically in an interesting way.

It is Boden’s third form of creativity that is the more mysterious and elusive, and that is transformational creativity. This describes those rare moments that are complete game changers. Every art form has these gear shifts. Think of Picasso and Cubism, Schoenberg and atonality, Joyce and modernism. They are like phase changes, when water suddenly goes from a liquid to a gas. This was the image Goethe hit on when he sought to describe wrestling for two years with how to write The Sorrows of Young Werther, only for a chance event to act as a sudden catalyst: ‘At that instant, the plan of Werther was found; the whole shot together from all directions, and became a solid mass, as the water in a vase, which is just at the freezing point, is changed by the slightest concussion into ice.’

Quite often these transformational moments hinge on changing the rules of the game, or dropping an assumption that previous generations had been working under. The square of a number is always positive. All molecules come in long lines not chains. Music must be written inside a harmonic scale structure. Faces have eyes on either side of the nose. At first glance it would seem hard to program such a decisive break, and yet there is a meta-rule for this type of creativity. You start by dropping constraints and see what emerges. The art, the creative act, is to choose what to drop or what fresh constraint to introduce such that you end up with a new thing of value.

If I were asked to identify a transformational moment in mathematics, the creation of the square root of minus one in the mid-sixteenth century would be a good candidate. This was a number that many mathematicians believed did not exist. It was referred to as an imaginary number (a derogatory term Descartes came up with to indicate that of course there was no such thing). And yet its creation did not contradict previous mathematics. It turned out it had been our mistake to exclude it. How can a computer come up with the concept of the square root of minus one when the data it is fed will tell it that there is no number whose square can be negative? A truly creative act sometimes requires us to step outside the system and create a new reality. Can a complex algorithm do that?

The emergence of the Romantic movement in music is in many ways a catalogue of rule breaking. Instead of moving between close key signatures as Classical composers had done, new upstarts like Schubert chose to shift key in ways that deliberately broke expectations. Schumann left chords unresolved that Haydn or Mozart would have felt the need to complete. Chopin in turn composed dense moments of chromatic runs and challenged rhythmic expectations with his unusual accented passages and bending of tempos. The move from one musical movement to another: from Medieval to Baroque to Classical to Romantic to Impressionist to Expressionist and beyond is a story of breaking the rules. Each movement is dependent on the one before to appreciate its creativity. It almost goes without saying that historical context plays an important role in allowing us to define something as new. Creativity is not an absolute but a relative activity. We are creative within our culture and frame of reference.

Can a computer initiate this kind of phase change and move us into a new musical or mathematical state? That seems a challenge. Algorithms learn how to act based on the data they interact with. Won’t this mean that they will always be condemned to producing more of the same?

As Picasso once said: ‘The chief enemy of creativity is good sense.’ That sounds on the face of it very much against the spirit of the machine. And yet you can program a system to behave irrationally. You can create a meta-rule that will instruct it to change course. As we shall see, this is in fact something machine learning is quite good at.