The Creativity Code. Marcus du Sautoy
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Why is it making that decision? The art it creates may provide a powerful lens through which to gain access to the subconscious decisions of the new code. And it may also reveal limitations and dangers that are inherent in creating code that we don’t fully understand.
There is another, more personal, reason for wanting to go on this journey. I am going through a very existential crisis. I have found myself wondering, with the onslaught of new developments in AI, if the job of mathematician will still be available to humans in decades to come. Mathematics is a subject of numbers and logic. Isn’t that what a computer does best?
Part of my defence against the computers knocking on the door of the department, wanting their place at the table, is that as much as mathematics is about numbers and logic, it is a highly creative subject, involving beauty and aesthetics. I want to argue in this book that the mathematics we share in our seminars and journals isn’t just the result of humans cranking a mechanical handle. Intuition and artistic sensitivity are important qualities for making a good mathematician. Surely these are traits that can never be programmed into a machine. Or can they?
This is why, as a mathematician, I am attentive to how successful the new AI is being in gaining entry to the world’s galleries, concert halls and publishing houses. The great German mathematician Karl Weierstrass once wrote: ‘a mathematician that is not something of a poet will never be a true mathematician.’ As Ada Lovelace perfectly encapsulates, you need a bit of Byron as much as Babbage. Although she thought machines were limited, Lovelace began to realise the potential of these machines of cogs and gears to express a more artistic side of its character:
It might act upon other things besides number … supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.
Yet she believed that any act of creativity would lie with the coder, not the machine. Is it possible to shift the weight of responsibility more towards the code? The current generation of coders believes it is.
At the dawn of AI, Alan Turing famously proposed a test to measure intelligence in a computer. I would now like to propose a new test: the Lovelace Test. To pass the Lovelace Test, an algorithm must originate a creative work of art such that the process is repeatable (i.e. it isn’t the result of a hardware error) and yet the programmer is unable to explain how the algorithm produced its output. This is what we are challenging the machines to do: to come up with something new, surprising and of value. For a machine to be deemed truly creative requires one extra step: its contribution should be more than an expression of the coder’s creativity or that of the person who built the data set. That is the challenge Ada Lovelace believed was insurmountable.
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: