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Preface xi

was a breakdown in communication. Of course, this may be a purely personal failing, but when I talk to people in other companies they report the same problem. It seems we all find communication difficult.

have wondered for many years why it is called the ‘art of communication’. Surely it’s a science, governed by bits, bytes and bandwidth. That might be true of the symbols in an email – they are clearly encoded symbolically – but is the understanding in our brains simply encoded by symbols? What is the physics that underlies human understanding?

Each summer I go on holiday to escape engineering for a couple of weeks. While away I indulge my passion for reading books by the likes of Douglas Hofstadter, David Deutsch and Stephen Hawking. One book that struck me years ago was Roger Penrose’s The Emperor’s New Mind. In it, he tackles the question of what happens in the human brain when we understand something. He extends an idea put forward by J.R. Lucas of Oxford University that minds must be more powerful than computers because they do something computers cannot: namely to step beyond mere rules and see truth. Colloquially we call this ‘common sense’ or ‘stepping outside the box’.

The Lucas argument uses the theories of Gödel and Turing to show computer algorithms have limitations. Some things are simply not computable. Computers can do many useful things, but they cannot discover new mathematical theorems, such as a proof of Fermat’s Last Theorem. In 1996, Andrew Wiles succeeded in finding a solution to this problem. This presents a paradox, solved only if we conclude Andrew Wiles is not a computer. Indeed, since most mathematicians discover at least one theorem during their lives, we must conclude no mathematician is a computer! This is controversial. Most philosophers tend to the view put forward by Daniel Dennett that the Universe is an entirely determined place and any personal sense of free will and creativity is an illusion. In Dennett’s worldview, Andrew Wiles is a special purpose machine that was always destined to solve Fermat’s Last Theorem. I believe this model is flawed. It is my aim in this book to show you why. Indeed I am going to go further and argue all human creativity is non-computational; art, communication, understanding – all are based on non-algorithmic principles.

If you consider creative thinking deeply enough you’re inevitably drawn into the question of whether we have free will. When I get to work each morning, the first thing I do – after a cup of coffee, obviously – is choose which creative task to tackle first. I feel this choice is freely made, but the determined determinists assure me I am wrong and my

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