The old man looked up from his work, and across the valley to where the foothills of the Great Mountains swept down onto the plains far to the west. The sun was hardly visible above the peaks now but for the moment at least, the village was still bathed in a luxuriously warm evening glow. The old man was only just in time. He looked down at the small piece of wood sitting in the palm of his brown, weathered hand. He then carefully carved the final markings on his miniature sculpture and put it down next to the others. His deeply lined face creased into an expression of satisfaction. And so it might because it had been six months of difficult and secretive work. But without warning his pleasure turned to sadness, and for a moment he felt as empty and lonely as the great plain to the West. He wished more than anything that his wife could be here with him to see the day, yet he knew better than anyone that it was impossible. The light was failing fast now, and he could already see a group of children running and skipping back down the dusty track towards the village. With his failing sight the old man could not tell whether his own son was amongst them, but he knew the boy would not be too late. Not tonight, because tomorrow was his tenth birthday. He turned his face again towards the dry expanse of the plain. The sun had been baking it all day, and now the breath from the mountains blew in as a warm and soothing breeze, carrying with it all the mysterious and distant sounds of the Himalaya. Today, in his peculiar state of contented melancholy, he fancied he could hear the very voice of God whispering to all who cared or dared to listen. Leaning heavily on his crooked stick, he made his way through the small door of his shelter, and made ready for bed.

As the first rays of light fell on the village and the early morning mist began to rise up from the valley floor, the small boy opened his eyes. He looked down to the foot of his bed and saw for the first time what the old man had secretly left there for him the night before. His face lit up with excitement. The carving was beautiful, and the pattern on the wooden base charming. Exactly what it was he had no idea, but it was the most wonderfully detailed thing he had ever seen. The old man woke and saw the excitement in the little boy's face.

The boy spoke in ancient Chinese. "What is it, father?", he asked.

"The Little Battle", whispered the old man.

In ten years time the name would be forgotten forever. But history would choose to find another name for the old man's creation - a name that would endure for the next thousand years, and then ten thousand after that. The name of 'Chess'.

The mathematician looked out through the lead-crossed window and across the immaculately kept lawns and magnificent spires of Cambridge university. The war was finally over, and although never fighting on the front line, he himself had probably been the most significant member of the Allied forces in saving the battle of the Atlantic. He turned and spoke to his friend and colleague who was reclining in a well worn leather armchair and puffing thoughtfully on his favourite deep-bowled pipe.

"Yes, but in principle? Could it be done in principle?", the first man said.

The other settled back in the armchair, took a long draw on his pipe and sent clouds of thick acrid smoke into the room. "I still say its highly doubtful. You seem to be forgetting one important assumption - the human brain is necessarily very different from any other kind of machine. You know how much I think of your new ideas, but you must accept that it is incumbent on every responsible mathematician to separate that which is theoretically sound from that which is merely speculation."

The Cambridge fellow begged to differ. "We have here the basis of a machine that, in theory, can process any mathematically computable function no matter how long or complicated. Now clearly there are functions which will take too long or require too much storage to be ever practically feasible, and I am fully prepared to accept that this particular problem may be one of these functions, but the question here is whether this theoretical machine could, given enough time and resources, play chess at a higher level than the best human player."

"My dear fellow, I am well aware of the question, but must still ask you to reconsider your reasoning." He re-lit his pipe and puffed energetically on it for a minute. "What we have to remember is that the human brain probably does much more than compute mathematical functions. Playing chess requires ingenuity, tactics and planning". He stood up and tossed the used match into the fire. He removed his pipe from his mouth and lowered his voice to finish his point: "It requires imagination, manipulation, strategy. The player must be aware of the subtleties of their opponent's schemes and traps. You must see that these are all very human characteristics, and not those which are easily transfered to a machine, no matter how advanced that machine happens to be."

But the old war hero stood his ground. "But what if chess is just another mathematical function, like any that you or I consider every day of our lives. My Universal Machine would then be able to calculate the best possible moves, looking so deep into the mechanics of the game that no human, no matter how inventive, could hope to match it."

His friend was shaking his head vehemently, but the other continued...

"After all, from any board position there are a fixed number of possibilities. All the machine would have to do is explore all these possibilities and pick the route that leads to highest likelihood of winning the game. This is a finite problem - this is my point - the rules of chess dictate that any game will only last a finite length of time, and there are only a finite number of different board positions. Therefore....". He took along intake of breath. "...therefore...my machine could, given enough time - and I accept it would be an infeasibly large amount of time - process the board position and come up with the best logical move possible...In THEORY, its possible"

The other man looked exasperated. "Well, maybe you're right, but I still say that a machine could never be expected to beat a good human chess player. Chess is a microcosm of human endeavour. You know that the game was probably invented by the Emperor of an ancient civilisation to train his generals in the art of battle strategy? Chess represents the very pinnacle of human faculty. The day someone produces a machine that can beat us all at chess will be the day machines are more intelligent than us. And if machines ever become more intelligent than us, then God help us!..."

In the nine years before his suicide, Alan Turing perfected his theory of what could and what could not be computed on a machine, and in so doing provided the theoretical cornerstone of all modern computing techniques. However, he never produced a machine that could play Grand-Master chess.

The boy looked at the board position that his father had been studying for the last week. It was, the boy's father had declared exasperatedly only the night before, "either impossible, or else the hardest chess problem in existence". It was supposedly checkmate in three moves with white to play. The boy had understood chess ever since learning the moves by watching his father play, but what confused him was why his father had not seen the obvious. He had always been told to help his parents where possible, so he reached out and moved white's last remaining Knight to King-Bishop Four. Now black had to move either his Rook or his queen, but in either case checkmate was imminent. His father suddenly noticed the two year old boy at the chessboard.

"Come away from there, Gary, you'll knock the board over!", he shouted.

Mr Kasparov then sat down to have his tea.

It was 11th May 1997 and the packed auditorium was itching with anticipation. Everyone had an opinion on what was about to happen, and some were expressing these opinions very vociferously indeed. The television cameras were in place, the radio microphones switched on, and the stage finally arranged to everyone's satisfaction after a full hour of impromptu wrangling over the precise seating arrangements. On the other end of the television cameras, twenty million cups of tea sat on twenty million coffee tables around the globe. The world was watched and waited. Without introduction, a man in a dark grey suit suddenly walked briskly onto the stage. The room erupted into wild applause and a thousand cheers, shouts and whistles deafened the television and radio microphones. But the man did nothing to acknowledge the audience. He did not say anything, or even glance once in their direction. Instead, he walked to the centre of the stage and sat down in his precisely positioned chair. The audience were undeterred by this apparent indifference and cheered even louder. They had come to see the greatest ever chess genius take on the first ever Grand Master chess machine. In one corner it was Gary Kasparov; in the other it was 'Deep Blue' - a supercomputer built in a laboratory at IBM.

To call Deep Blue a machine was actually misleading, because in fact it was many machines - hundreds of computers slotted into a huge frame which sat in the corner of the stage. A human representative for Deep Blue would read the output from the computer and then move the appropriate piece on the chess board in front of Kasparov. The man himself had been playing ever since he was two years old, and had honed his unique intuition for the game over years and years of play against the world's strongest proponents of the game. The computer, in contrast, had little experience of the game or any of its top players. It hadn't even existed a few months before. But in compensation, each little computer inside that frame calculated millions of possible board positions every second. The styles were very different, but the rules and objective of the game were identical for both.

The match was finely poised at two and a half points each, with the play so far always going with the pieces. In this last game Kasparov was playing white, and so the advantage was back with him. A hush descended over the crowd as the giant computerised chess-board above the stage was switched on. Sixteen pieces could be clearly seen lined up in two neat rows on either side of the board, with an empty expanse of squares in-between on which the battle would take place. Across the world people settled uneasily into their armchairs to watch this ultimate battle between mind and machine.

The clock was started, and Kasparov moved his King Pawn two spaces. Deep Blue responded immediately with a pawn move of its own. The giant computer screen was updated automatically, but there was a brief pause as the official moved the piece on Kasparov's board. Kasparov made a second move without further delay, and Deep Blue again responded without a pause of any kind. The first few moves were straight out of the opening book. A thousand years of playing experience had taught which opening lines were best. Kasparov had spent a lifetime memorising these opening game moves, and the machine had had them built into its electronic memory. Another pawn was moved by Kasparov, then a Knight was brought into play by the computer. The audience watched in terrified anticipation. Surely Kasparov would ultimately triumph over the machine. The chess prodigy looked out over the sea of eager faces and in so doing suddenly felt the expectations and fears of the whole world weighing heavily on his mountainous shoulders. In the rigid stillness of the auditorium, he could see them all breathing, almost as if they were one huge living organism. Kasparov looked back to the board and moved his queen Knight, but this time the machine paused for some minutes before responding using its black-squared bishop. They were out of the opening book, and so now it was down to pure strategy on the part of both contenders.

After ten moves each, the experts judged the position to be equitable at worse for Kasparov, and probably slightly in his favour, but the machine played on undaunted. As Kasparov made his eleventh move, the sound of the piece being placed back on the board could be heard clearly at the back of the auditorium. The computer thought for seven minutes and thirty-six seconds before replying with a daring piece sacrifice. Murmurs and gasps from the audience momentarily broke the silence. Had the machine somehow made a mistake in its calculations? Kasparov could take the piece, but the computer was banking on a better positional play in compensation. Kasparov thought long and hard before accepting the challenge. The machine then swapped two more pieces with the human after which it was still material down, but with two connected passed pawns with nothing to block their path to the far end of the board and victory. On move thirteen, Kasparov's position looked uncomfortable, and the man himself was visibly sweating under the scrutiny of the stage lights. He glanced again at the audience. In the awful silence, he could hear them breathing on the front row. He suddenly felt as if he could even feel their breath falling on his face.

But the computer felt nothing as it advanced one of the pawns by one more square. By move fifteen the experts were worried too. By move sixteen Kasparov had developed a deep and apparently permanent frown on his huge forehead. Kasparov sacrificed his Rook on square E6 on move seventeen to attempt to redress the positional imbalance. But the computer just moved the pawn one more square forwards. The material was exactly equal now, but the positional advantage of those pawns meant the outcome was weighted heavily in the favour of Deep Blue. With the aid of their toy computers, the experts in the commentary box were plotting possible lines for the human player. One thought he might even have seen a way to escape. The shock came on move nineteen. The world held its breath as Kasparov reached out his hand and picked up his piece. Then he let the King drop onto the board with a clatter - a clatter which was to be heard by the whole of mankind. The game and match was over - he had resigned. The room was in uproar, but he had just been the second to see the inevitability of the position. The first to see this inevitability sat motionless, until eventually someone from IBM came to switch it off.

The huge wrought-iron gates swung open on their monstrous hinges. Mr Polani walked through looking up at the sign as he did so. It read:

and underneath in smaller letters: 'Research and Development'. He made his way up a smoothly tarmacked, picturesque avenue lined with Birch trees that radiated green and silver in the warm summer sun. He had travelled all the way from Europe for this meeting, and as he rounded the gentle sweep of the drive, and as the imposing sight of the super-modern tinted-glass building appeared between the trees, he began to feel ever so slightly nervous. What if they didn't think his idea was credible, or worse, what if they laughed at him for even suggesting that such a thing was possible. After all he didn't know that much about computers - his considerable expertise lay elsewhere. He walked up the steps to the front of the building, and through one of the sliding doors that opened automatically for him. Inside he found himself in a large foyer which looked more like the lobby of an exceedingly posh hotel. The whole entrance was bathed in sunlight, and living plants artistically arranged around the periphery gave the impression of being in a huge green house. Only the atmosphere wasn't stuffy and stifling, but a perfectly comfortable and precisely maintained ninety-eight point four degrees. A gleaming blue-white marble floor gave his small shoes a crisp, clean feel as he approached the reception desk. He introduced himself to the girl sitting behind it.

"Good Morning, I'm Franz Polani - here to see Dr Robert Hallam."

The girl's reply was bright and friendly. "Thankyou Sir, please take a seat. He'll be down in a moment."

The man made his way to a plush black sofa that was sheltering under what looked like a banana tree. He perched primly on the edge of the sofa and decided he felt very satisfied with his first impressions of clean-cut intellectual creativity. While he waited, he turned his grand idea over in his mind for the umpteenth time.

Franz Polani was a musical genius. He had played his first ever note on the piano at just six months when, in his mother's arms, his right foot had come down heavily on C-sharp during a risky spring-cleaning manoeuvre in the music room. It was, by now, a famous joke, and the opening anecdote at most of his public appearances. But Polani's talents had turned out to be anything but a joke. At three he had taken the instrument up seriously. By four he was familiar with some of Beethoven's easy sonatas, by six with most of Chopin's Mazurkas, and by the age of ten he could play almost any Debussy he chose. The day before his Twelfth birthday, he had performed Rachmaninoff's second and third concertos back to back to a spellbound and disbelieving audience which had included all of the top pianists, conductors and composers of the day. They had marvelled not so much at his prodigious technical skill, but at his deep understanding of the music. Being able to press the right notes in the right order was something that every accomplished pianist could do given enough practice, but Polani had seemed to exhibit something entirely different. It was the way in which he had expressed every subtlety of the music with such a consistent touch yet with such deliciously original phrasing that had impressed his illustrious audience more than anything. It was the way he had made the piano sing as if were a human voice. What made Polani's achievement even more remarkable was that he had never had a music lesson in his life. Somehow it was in his blood and to some it really seemed as if he had been born to understand and appreciate music in a way no other person alive seemed able to do.

A tall man suddenly appeared in the foyer, took a quick look round, and then walked briskly over to where Polani was sitting.

"Sir Franz Polani! Hello, I'm Rob Hallam. Welcome to our lab."

As Robert Hallam extended his hand, Franz Polani rose to his feet offering not his own hand but instead a small and pompous bow.

"Thankyou, and thankyou for agreeing to see me.", said Polani in that slow, dry voice of his.

"Not at all, not at all. We're honoured here. You caused quite a bit of excitement you know, when your letter arrived. After all, its not often we get the world's greatest musician decide to visit our labs!". Hallam's quick dark eyes darted to and fro as he spoke.

Polani offered another austere little bow. Robert Hallam looked to be about thirty years younger than he, dressed as he was in an old pair of jeans and a loose fitting T-shirt. Somehow he looked rather incongruous in these surroundings, especially with his long untidy hair tied back in a pony-tail.

"How was your journey, Sir?", inquired Hallam politely.

``The journey was fine, thankyou - a little tiring perhaps.''

``Well, I'm glad you made it. Shall we go up to my office?''

The two men made their way up a flight of glass stairs and along a softly lit corridor before arriving in Hallam's neat and spacious office. In the centre of the room was a large oak desk which seemed to double as an impromptu bookcase. A real but overflowing bookcase was propped up against one wall, and a huge old fashioned white-board ran almost the full length of the opposite wall. Apart from an old and exhausted looking arm chair, the room was fairly empty, although Polani noticed a half open cupboard behind the main door which was absolutely full of gadgets and wires and bits of circuit-board and other mysterious looking equipment. The far wall of the room was made from a single sheet of glass which looked out over the most beautiful gardens behind the building. As Polani peered over his small spectacles at the grounds below, he could see that the centerpiece of the garden was a giant fountain that continuously changed the pattern of water it sent up into the air like some kind of huge living kaleidoscopic sculpture. Polani stood at the window and watched the water while his host pulled up a couple of chairs around the table.

"Right, what can I do for you? I must say you've had me in the most awful state of anticipation." Hallam illustrated the point by waving the original letter which Polani had written. "I wondered what on earth you could want from a research department like this."

Polani, turned to the other man with a sudden look of earnestness on his face.

"Do you like music?", he asked in his characteristic slow, dry voice.

Wondering whether this was some kind of test, Hallam thought for a bit before replying.

"Yes, I do", he said, "very much".

"Who's your favourite composer?"

Hallam thought again for a second.

"Bach", he said.

"Why do you like Bach?".

This time Hallam paused longer. If it had been anyone else asking these questions he might have thought the conversation a trifle odd. But he knew well of this man's reputation for eccentricity. He knew he was speaking to a musician of the highest possible calibre - one who had composed his first piano concerto before his tenth birthday. Again, he considered his reply carefully.

"Why do I like Bach....?'', he repeated rhetorically, ``I'm not sure I can quantify it. I suppose I like the structure of his music. He has a very principled, almost logical approach, yet there's immense artistry there too."

Polani made no reply and said nothing more for several moments. He was looking out of the window and seemed to be thinking. Hallam didn't quite know what to say or do next. There was something rather intense about his visitor, and he wondered whether his last answer might not have been in some way inappropriate. He decided to venture a question of his own.

"Do you like Bach?", he asked.

Polani looked back at Hallam. For a moment their eyes met in mutual interrogation. But Polani still didn't speak. He seemed to be thinking. Eventually he issued his reply.

"Yes", he said, "I too like his respect for structure and his principled approach to composition. I like the way in which he treats melody and harmony as two sides of the same coin; the way in which he is able to weave themes and variations on those themes together into an holistic musical fabric which far exceeds the sum of the parts. I like his passion for order."

"You speak as if he's still alive", said Hallam.

"He is", said the musician, his voice slower and drier than ever, "Every time I play his music".

The eccentric genius continued without even glancing in Hallam's direction.

"I adore the romantic lyricism of Chopin, the passion and insanity of Rachmaninoff. I love the intellectual exuberance of Liszt, without whom the piano would be half the instrument it is. How do you feel about his second Hungarian Rhapsody?"

"I'm not sure I know the piece", said Hallam, beginning to feel a little unsettled.

This didn't derail Polani in the slightest. He stood up and walked to the window before continuing.

"Beyond all others, I love the profound elegance of Wolfgang Amadeus Mozart - not just his piano music, but all his music from Opera to Orchestral. There seems to be something special about him above all others". He turned around again to address Hallam directly. "You know, some great composers were inspired by nature - they wrote about majestic mountains or the joy of the dawn, or the seasons, or even the planets. Other composers wrote music about comedy or suffering, love and death. But what makes Mozart stand out - above all others - is that he wrote music about music itself. When I play Mozart, I'm always left with an impression of infinite and unrivalled purity."

"I think I know what you mean. Some pieces do seem to have an enduring quality.", Hallam replied.

"Indeed they do, indeed they do", pondered Polani. Suddenly, he seemed to come down to earth because he turned directly to the other man and smiled a little. "I'm sorry", he said, "I sometimes get too carried away. I know you're wondering why I asked to see you. The truth is that I think you, and possibly only you, can help me. The company you work for is the largest designer and builder of computers by far. I have to admit that I don't know that much about computers, but I did do a little research, and I know that your group here are responsible for innovating completely new technologies. Am I right?"

"You are, on all counts. We're twice as big as our nearest rivals, and this building is allegedly the home of some of the finest research minds in the world.''. A cheeky wry smile played over the corners of Hallam's mouth as he waved his hands as if to draw attention to his surroundings. ``Our job is to build the new generation of technology that will one day become commonplace and indispensable to every household in the world. Well, that's the hope anyway."

"I've also been told that you are the finest computer expert here. The finest since Alan Turing, some say."

Rob Hallam was embarrassed and may have turned the faintest hint of pink. "Well, they've chosen to put me in charge of the lab, if that means anything", he said, "but that's really because I usually do what I'm told. Management like that you see."

Polani knew that the other man was being modest. He had spent some time looking for just the right person to approach with his proposition, and according to his sources Robert Hallam was that person. "They say you invented the first artificial neural computer, and also the first fully parallel optical supercomputer".

"Well, me and many others."

``I also know that you are musical. You like music.'', accused Polani.

``I learned the piano as a child, that's all. Honestly, I'm no better than half the ten year old children learning the piano from here to the West Coast.'', protested Hallam.

``Maybe, but its your computing genius that I'm really interested in. I want you to build something for me.''

Rob Hallam raised his eyebrows. It wasn't often someone came to him with a request. Not in his line of business. But quite what the world's greatest musician wanted him to build was beyond even his highly muscular imagination.

Polani waited for Hallam to look up again. He wanted to make sure he had the computer scientist's complete attention.

"Do you believe in the perfect piece of music?", he asked.

Hallam considered for a minute. "I'm not sure I do, I think music is a highly subjective thing. Perfect for one person may not be perfect for another. Anyway, what does perfect mean?"

"Let me tell you something", whispered Polani, almost as if he were imparting a great secret. "I've studied music for more than sixty years. I've played or conducted every piece of music written by every one of the great composers, and I'll tell you what I've concluded. I've concluded that there IS such a thing as the perfect piece of music. A construction so profound that Mozart himself would be forced to admit that for all his greatness he was only a pawn on the musical chessboard.''

Hallam was suddenly captured by the irresistible seriousness with which Polani spoke. The musician's voice had dried up almost to the point of cracking.

``I want you to help me find that perfect piece of music. I want you to help me discover the voice of God.''

A stunned silence descended over the cluttered office. For half a minute nobody seemed to dare speak. It was Polani who decided to break the silence.

``What do you think, could it be done?''

Hallam was slightly confused and very taken aback. It was by far the strangest thing he had ever been asked. ``Er...I don't see how. You have to understand that computers process data in a highly logical way. Surely you realise more than anyone that music is something entirely different.''

Polani's response was passionate. ``But music is logical - mathematical even - when considered in its purist form. Its about notes, their timing, and the intervals between them. Every piece is constructed from these basic spatial and temporal components, no matter what complexity or subtlety it goes on to achieve. Even Mozart was forced to restrict himself to such pragmatics issues. Melody and harmony, and the full blown phrases and semantics of the music must be built up out of these simple constituents, and it is these constituents that the computer would process.''

``But music is an art form, not a science'', retorted Hallam. ``It requires ingenuity, creativity, imagination. It requires a sense of feeling. Music embodies our own knowledge and understanding of the world. How could a machine possibly hope to produce anything meaningful.''

``I have a theory'', replied Polani, ``that music is discovered not created. All one has to do is look to find it, and then of course be able to recognise it when one does find it. The process is essentially one of search and not of invention. It is to perform this search that I wish you to build me a machine.''

``No, I don't follow. Its unthinkable. I can't see how....''

Polani interrupted him. ``Listen, I remember my Grandfather telling me about the days when they thought a machine could never beat the best human chess player. He told me how as a child he had sat on the front row, right up against the stage, and seen the then world champion beaten for the first time by a machine. It seems crazy now that people once thought a machine would never triumph at chess. As crazy as the thought of people expecting a person to be able to perform long division faster than a calculator. But now look, we have machines that can play a perfect game of chess. Machines that can search every possible board position to find the best moves. Machines that any man, no matter how clever, could only draw against. Just think about it for a moment.

Hallam thought. It was true that for some years machines had been able to play a theoretically perfect game of chess just by searching through all possible board positions. But he wasn't sure how this related to music.

``Of course, chess is a finite game.'', he said.

``Exactly!'', said Polani triumphantly, ``But what I've come to realise is that music is the same too, just on a much larger scale.''

``You mean to say that music is some great game?''

Polani's voice croaked and cracked like an old broken down engine that was turning over again for the first time in years. ``No, not a great game'', he said, ``The greatest game.''

The scientist had risen from his chair and was pacing around the room in an air of intellectual chaos. Relentlessly, Polani turned to follow him around the room. ``I'll prove to you that music is a finite game. How many notes are there on a piano?''

Hallam muttered as he paced: ``Eighty-eight, isn't it?''

``Yes, Eighty-eight. Now, let us say that the average piece contains no more than a thousand notes - but pick any number you like - that gives us a strictly finite number of different combinations of notes. Now imagine writing every single possible combination of notes on a separate page and lining the pages up next to each other. It would be like trying to arrange a chess board into every possible combination, only much much more complicated.''

Still pacing up and down, Hallam nodded his head. ``Yes, that's right, there are eighty-eight keys on a piano, but only sixty four squares on a chess board. Plus there are only thirty-two chess pieces, but potentially thousands of notes in a piece of music.''

Polani continued. ``Now, if you lined up all these musical combinations, you'd have an unimaginable number of pieces, but every piece ever written, and every piece that could ever be written would be there. Most would make no sense whatsoever, but in amongst all that random rubbish, some would be the known classics of Mozart, Bach, Liszt. But these would only be a tiny and impoverished minority of what would be on display. There would be pieces of music there that nobody had every imagined. There would be pieces of music so beautiful that nobody ever could imagine them. And one of those pieces would be absolutely perfect.''

Hallam stopped pacing for a moment, and looked at Polani in a mixture of confusion and disbelief. ``No, its too difficult...the numbers are astronomical''.

But Polani was undeterred. ``I want you to build a computer that we can use to enumerate every sensible musical piece, in exactly the same way that a chess computer enumerates every possible board position. Just tell me, is it possible - in theory at least.''

Hallam was now shaking his head wildly. ``Listen, the numbers are just too large...of course its possible in theory. Its easily computable according to Turing's theory, but in practice...I just don't know...''. He paused and thought for a moment. Then he grabbed a pen from his desk and began writing on his white-board, muttering to himself as he did so. ``Right, eighty-eight keys, and a thousand notes...''. Some formulae appeared, then some more numbers. He stepped back from the board every now and then to consider what he had written so far. ``So...we'd have to recurse to the tenth level - maybe the fifteenth to be absolutely sure...''. More lines and symbols appeared with the odd arrow to link his steps of reasoning. It made no sense whatsoever to Polani, who just sat and waited. Finally, Hallam wrote a number on the board. The number, which stretched from one end of the room to the other, had so many zeros on the end of it that there was hardly space for them all. He stepped completely back from his work and turned to Polani. ``This is roughly how many pieces of music we would need to look at, with each containing no more than one thousand notes. A full scale symphony or Opera would contain many more.''

Polani looked at the other's calculation. ``OK, lets ignore the largest pieces for the time being. Let's just consider relatively short piano works. After all, the perfect piece of music needn't be long. In fact, it probably shouldn't be long. Now tell me Mr Hallam, can it be done. Can the largest computer generate that many combinations?''

``Not at the moment, that's for sure. It'd need something a thousand times more powerful than we have at the moment. We'd need some kind of array of optical supercomputers, probably linked to a parallel base of neural computers. But we'd still need a new technology for the analysis kernel. You realise this would need to be the biggest computer every built - bigger than everything they have at the government's defence and space agencies combined.''

``Then it can be done?'', suggested Polani, encouragingly.

``Perhaps, in theory. But simply generating every musical combination isn't enough. How would we know if we had found the perfect one?''

``That's where I can help. You see I know what the ingredients are, its just the recipe I can't find. Just like chess computers need to be fed basic information about the game by an expert, I will donate all my expertise to this computer. Remember, we don't have to actually create the piece, just recognise it when we find it, and that is a much simpler problem.''

``Yes, I see...it might work. After all, chess machines are able to play better chess than their human creators. In fact modern chess machines are only given the basic rules of the game - the rest they derive for themselves.''

For the first time, Polani suddenly gave a broad smile. ``Right! And I will provide the rules of this game - the rules of music, as it were.''

Hallam frowned. ``Yes, but I still don't understand how these rules can define what makes an ultimate piece of music. After all, surely its all a matter of taste. Its subjective. Some people love music that other's can't stand, or at best are indifferent to. How can you be sure of what is universally best.''

But Polani had an answer ready. ``Yes of course, some like classical music, while others like pop or jazz, but have you ever asked yourself why some music survives generation after generation, and other music, although it might seem popular at the time, fails to survive the test of time.''

Polani didn't wait for an answer.

``Whatever your views on the great classical composers, have you ever wondered why the likes of Mozart and Chopin and Bach are actually played more with every passing year, not less, and by every culture on the face of the earth.''

Again, Polani wasn't interested in Hallam's answer.

``I'll tell you why'', he continued, ``It's because these pieces, these musical discoveries if you like, have a universal quality. We know it must be a quality that transcends the fashions of the time, that completely bypasses cultural differences. Age...gender...class...they're all meaningless to great music. There is a truth in music - a mathematical truth - that is as inescapable as the answer to two plus two. It is this truth that I want to attain. Listen:''

Suddenly Polani started singing the musical scale:

``Doh...ray...me...fah...soh...lah...te...''. He stopped one note before the end.

``Sing the last note'', he suddenly demanded.

``What?''

``Sing the last note.''

Hallam reluctantly did as he was told. ''...doh''.

``Now how did you know that?'', interrogated Polani.

``Well, its the last note of the scale. Everybody knows that. It just sounds right.'', Hallam replied.

Polani was visibly excited. ``Exactly'', he cried. ``Its a fundamental truth, defined in the mathematics of music. Did you know - that's how Beethoven's father used to get the young composer out of bed in the morning. He would play those first seven notes on the piano, and Ludwig would be so obsessed by it that he would have to get up to finish the scale off! My point is that there are patterns to music that everybody recognises as truth.''

But Hallam wasn't going to give up that easily.

``So why are there some people who don't appreciate even the most famous pieces of music'', he argued.

Polani lowered his voice back to its familiar dry crackle.

``All music we have today is far from perfect. All those little mathematical inaccuracies add up, and some people just can't complete the scale. The perfect piece of music will be understood and appreciated by practically everyone as easily as they can sing the last note to the scale, or say that the answer to 'two plus two' is four.''

``Perhaps, you're right'', conceded Hallam, but there's no way to prove it - well, not unless we could find the piece that you're talking about.''.

``Which is therefore what we must try to do. Look at it this way. Not everyone plays the same game of chess, or even to anywhere near the same standard, but that doesn't stop there being a perfect strategy that can beat even the best player. I want to create that perfect musical strategy which is vindicated by the very proofs of mathematics itself.''

Hallam wasn't sure what to say. He wasn't sure whether Polani was right, or else just plain mad, but he was certainly curious to find out. But then he frowned again as he realised another drawback.

``You realise that the cost of building a computer this big would be astronomical! They'd never fund it. Not just as some kind of hobbyist's adventure. Maybe if it had defence implications...no but even then...''

``But it'll have huge commercial implications'', suggested Polani. ``Think about it. If it works, the world will have an almost endless supply of the greatest music that its possible to hear. Living composers, past and present, will be relegated to a small historical section in the music shops around the world. There'll be no more waiting for someone to invent the next great piece of music...Any style, any genre, the world would pay a fortune for the luxury. It would revolutionise the music industry from pop to classical. We'll probably even invent a huge number of new musical genres. The possibilities for the whole of humanity are endless. Think of the prestige for you and your company.''

The computer scientist had to admit that the ramifications were truly huge. Maybe given the potential of trillion-dollar profit margins, the management might agree to stump up the massive investment. He smiled at Polani, who, he suddenly realised, was not just eccentric, but absolutely insane. Polani smiled back politely.

``OK, Mr Polani, I'll draw up a proposal for the managers. This one is so big that it'll need to be run past the shareholders too. I'll let you know what the outcome is.''

With that, Franz Polani left Parallel Technologies Ltd. and returned to his hotel. There was a grand piano in the hotel lobby, but he decided that since it was such a lovely afternoon, he would go fishing on the lake instead.

Exactly a week after his first encounter with Robert Hallam, Polani had been walking through his hotel lobby when the receptionist had run over and handed him a message. It had read:

`Mr Polani, please come over at the first opportunity. I'm in all day today. Rob Hallam.'

An hour later he found himself back at the iron gates of the renown research and development centre. He walked back up the sweeping bend of the drive, up the steps, through the sliding doors and into the reception. As he had done the week before, he announced his arrival to the girl behind the desk, who this time told him to go straight up. A minute later he was standing back in Hallam's office. Hallam himself seemed to be frantically looking for something, but what grabbed Polani's attention was the state of the room. It looked as though it had been ransacked from top to bottom. The table had been moved from the centre, and was now almost hidden under ream after ream of computer printout and other paper. The books sitting on the desk had trebled in number since the previous week, and were now lying all over the place, some open face up, some open face down, and others standing in various disordered piles. The white-board was full of formulae and diagrams scrawled in incoherent signs and symbols, none of which made the least sense to Polani. To add to the chaos, fragments of cannibalised machinery lay scattered over the floor, and it was for one of these bits of machinery that Hallam seemed to be looking. But at the sight of Polani he stopped looking. He let go of the cupboard door, stood up, and instinctively greeted the visitor by extending his hand. This time the musician shook it.

``Good to see you again, Mr Polani. Take a seat, please.''

He waved his hand in the direction of the most chaotic corner of the room in which somewhere, presumably, there were some chairs. Hallam, still out of breath from his energetic search, hastily cleared some space for them to sit.

``I got your message this morning.'', said Polani. ``I hope its good news.''

``Good news? You could say that'', breathed Hallam with excitement. ``They've gone and given us the go ahead. I costed it up and they had an emergency meeting with the shareholders. And then first thing this morning the managers called me in to say we had permission to proceed. They were rather excited about it too. They think it has the potential to be the biggest thing this company has ever done. They thought the marketing opportunities were phenomenal...''

Inside, Polani felt almost overcome with joy. It had been a long week waiting for the verdict. ``So what do we do now?'', he said drily.

``Right! I'm going to have to build something quite new. It'll need most of this floor to house it. We've got three machine rooms we can use, and we'll convert the lab at the end to a music studio. You can work in there, giving us the information to put into the supercomputer. My team and I will build the machine itself.''

Hallam suddenly produced a detailed diagram from under a mass of paper. ``It'll be the first ever Neuro-Optic device. You know that the human brain works by millions of millions of tiny wires called `neurons' interconnecting in complex configurations. Each neuron transmits a small amount of electricity which it passes on to the other neurons to which its connected....well, the new machine is based on the same principle, but will use light itself as the means for communication. This way we get a much faster clock speed. There'll be an array of conventional computers to manage the multiplexing...then we'll have a central supercomputer to coordinate the....''

Hallam suddenly noticed that he had lost Polani somewhere along the way. ``Oh sorry, well it doesn't matter really. What you have to do is provide those rules of music, as you put it. If you like - we'll search those chess board positions, and you can explain how we tell the winning ones from the others!''

``Very good'', said Polani confidently. Although he might not have looked it, he was truly overjoyed at the prospect of his idea being put into practice. Ideas which had been developing in that peculiar mind of his for best part of half a century, and now at last, it was time to put them to the test.

``Now, there's lots to arrange. They've only given us a year's budget to start with, so there's no time to lose. Come with me, I'll show you where we will work...''

During the next fortnight, Parallel Technologies was a hive of activity. Internal walls were brought down, offices were converted, a music laboratory created, a grand piano installed, and extra staff hired. Dozens of companies from all over the world delivered hundreds of pieces of specialist equipment through those large wrought iron gates and up that sweeping drive. Most had to be made specifically to order: Three optical generators, a neural encoder-decoder set, over twenty miles worth of electrical cable, nearly one hundred miles of optic fibre, five dozen quantum generators, fifty laser machined prisms, almost forty-thousand nano-circuit boards. Piano tuners came and went. Piano repairers came and went. Musicians from all over the world were invited to offer their particular specialist knowledge. In the months that followed, technicians, electronics experts, computer scientists, neurologists, programmers and musicians worked in shifts around the clock on the most exciting engineering project mankind had embarked upon since the first ever moon landing.

Inside the lab, Polani, who had had to move his entire studio to the other side of the world in order to participate in the project, worked sixteen hour days supplying the information that was required. He formalised his musical theory, cross referencing piece after piece of musical data. Most of the patterns were obvious to his heightened musical senses, but occasionally even he would get stuck on the smallest points of detail. Slowly the data took shape. To anyone other than him his work was completely inscrutable, and Hallam had little or no understanding of Polani's theory despite the other's numerous attempts to explain it. But that didn't matter. As the first ever neuro-optic supercomputer was being built next door, so the first ever complete musical theory was being formulated. Finally, after more than six months of work it was time to start feeding data into the memory banks. Day after day and night after night, Polani's symbols were painstakingly translated into the computer's own binary language of ones and zeros.

By late June, the year after Polani's first visit to Parallel Technologies, the machine was finally finished, and all of Polani's musical theory transcribed and entered into the computer's memory. All that remained was to switch on the main grid of optical supercomputers, and for this momentous occasion the entire senior lab staff had gathered in the main machine room. They were all aware that it would take a huge time for the machine to generate what they were looking for, but the process of starting it off was being viewed as a major event - rather like switching on the Christmas tree lights four weeks before Christmas. Hallam himself was buzzing around with a huge smile on his face making final alterations here or there - or at least pretending to - while Polani paced small nervous steps up and down the lab.

``OK, Henderson, I think we're ready to go. Better get on the power switch. Polani, do you want to come over and watch.''

Mr Polani walked over. There were four entire rooms of support machines, but the main optical supercomputer sitting in front of them was little bigger than a box of chocolates. It seemed funny to think that they were pinning their hopes on such a small device, no matter how sophisticated it happened to be. Everyone assembled and stopped what they were doing, as if marking their respect. The output tray of the machine would be empty for weeks and probably months, but it was still terribly exciting because this was the first time the whole ensemble had been tested together. Everyone was nervous because nobody wanted it to be their bit of the machine that went wrong. They all stood in respectful silence for a few seconds, then Hallam nodded to the chief engineer who pulled the power switch.

For a second nothing happened, then the lights went out and the room was cast into darkness. Suddenly there was an awful sound of splintering from the machine, followed by Hallam's excited voice screeching out into the darkness.

``Cut the power, Henderson. Its drawing too much power. CUT THE POWER!''

But before Henderson had had time to do anything, there was a bang from the direction of the box of chocolates, and the room was suddenly lit up by a kaleidoscope of multi-coloured and ultra-violet light, shining onto the walls and ceiling from out of the heart of the optical computer. At the same moment, Henderson dropped the power switch, and the room was thrown back into complete darkness, but it was too late. The damage appeared to have been done.

``DAMN!'', cried Hallam, ``It shouldn't have been drawing that much power.''

``What on earth's happened? Has it blown up?'', asked a distraught Polani.

``Something's gone, that's for sure'', replied the scientist. ``For goodness sake someone put the emergency lighting on.''

The lights came up a moment or two later to reveal ten of the most disappointed faces in the country. Henderson was walking back from the emergency power switch, Polani was standing motionless with a deep frown on his face, Hallam was peering into the machine through a pair of dark goggles, and the others were hovering nervously in case the verdict came that some oversight on their part was responsible for the destruction of a piece of equipment that had taken over a hundred and fifty thousand man hours, twelve months, and nearly one billion dollars to build. But it was a full two days later before the actual verdict came.

``Well, Polani, its just one of those things I'm afraid. An oversight you might say, but given that this is the first time a machine like this has ever been constructed, I suppose some oversights are inevitable.''

``How long did you say it will take to repair?''

``Hmm, hard to say, three months probably. Maybe two if we're lucky. We've got to get some new parts in. I take full responsibility for it. I had no idea it would draw that much power.''

Polani sighed. It was bad enough knowing that it would take at least a month for the machine to generate its output, but now knowing it would be at least two more before the computer could even be started, was exceedingly frustrating.

``Why don't you take a holiday for a bit?'', suggested Hallam, ``We'll carry on the work here. You've done all you can for now.

Polani had been so engrossed in his work that he hadn't been back home for nearly a year. Maybe Hallam's idea was a good one. He had been missed in the concert halls of Europe while he had been working on this project. It might even take his mind off things for a while.

``Yes, I think I will.'' he replied.

In fact it was nearly four months before Polani received a transatlantic call from Hallam saying they were almost ready to try again. In the meantime, the musician had done exactly what he had planned and taken a much needed holiday. During his break he had delighted audiences in almost every prestigious concert hall across Europe with his recitals of Liszt, Rachmaninoff, Chopin and Beethoven. But he told nobody of his project on the other side of the world, and nobody could even have guessed at how he planned to revolutionise music itself.

The day after the phone call, Polani was back at Hallam's lab. The setup looked very similar to before, but this time only Henderson and three other technicians were present. This time nobody seemed to be relishing the drama of the event, and Hallam wasn't looking anywhere near as confident as he had done four months previously. This time the mood seemed far more sombre as Hallam signalled to Henderson to pull the switch. There was a clank as the switch was driven home. For a second nothing happened. Then there was a series of beeps and a green light appeared on the main control panel of the supercomputer. Then a number appeared in blue on the same display. It said: ``0''. A loud cheer broke out.

The number suddenly started changing, slowly at first, but then faster and faster. Soon it changed so quickly that the digits to the far right were completely unreadable.

``That's the counter'', Hallam explained to Polani, ``It lets us know how many pieces of music have been searched, and how long there is to go.''

Polani looked on, fascinated by the little box of chocolates, silently doing its work.

``I am afraid, good people'', said Hallam triumphantly, ``that now we must just wait''.

But waiting turned out to be the hardest thing Polani had ever done. As the machine searched a quadrillion pieces of music every second, the musical genius tried in vain to occupy himself as best he could. Some days he went fishing, other days he went for long walks. When he felt like it, he gave recitals. Some days he went into the lab, and watched the machine work. When he was away from the lab he was terrified of getting a message to say the machine had blown up, or melted down, or been stolen, or someone had pulled the plug accidentally, or spilt a cup of coffee over it. The hours passed excruciatingly slowly, and yet went slower and slower with every passing day. The days felt like weeks, and the weeks like whole years. But the machine experienced every nano-second with complete indifference. Its steady and predictable temperament patiently and faithfully examined sequence after sequence of ones and zeros, each represented by infinitesimal pulses of light. It didn't get bored, or frustrated, or nervous, or excited. By the end of the first week it had discovered the first well known classic, as well as a million minor variations. Quite unbeknownst to its creators, on the second Tuesday after power had first coursed through its neural-optic circuitry, it discovered Beethoven's moonlight sonata. Then Mozart, and Chopin, and Liszt and all the other great composers. Some pieces the computer discovered made no sense at all, others were beautiful. But the computer didn't notice. It just performed sum after sum, calculation after calculation. The light inside the machine shone brightly night after night.

It wasn't until six weeks later, and a full eighteen months since Polani had first set foot in the grounds of Parallel Technologies, that the message arrived at last. It read:

``Franz, come at once. Rob.''

Something had gone wrong, he was sure. Why else would Rob be so vague, and why else would he have contacted his hotel so late at night. He arrived at the gates of the lab in record time from the hotel. He entered the code and hurried up the sweeping drive, taking the steps two at a time. He ran across the reception foyer, and straight up the glass stairway at the far end. A minute later he was standing again in Hallam's office.

``Follow me!'', said the scientist. He had a broad smile on his face, and was so agitated he couldn't seem to keep both feet on the floor at the same time. The two men made their way to the machine room. Everyone had gone home for the evening long ago, and the place was deserted. Hallam's eyes darted to and fro with pure excitement.

``Look!'', he said.

Polani looked down to where the other was pointing. As he did so, his heart rate stepped up a gear. The green light on the control panel was no longer on, and the counter had stopped having reached a number so huge that it would have taken a minute to even read it out. But what excited both men more than anything was a pile of paper sitting in the supercomputer's output tray. Polani uncontrollably reached out and picked it up. It was music. Sheet after sheet of musical notation. Two pairs of eyes scanned the lines for some kind of vital clue to indicate whether or not they had been successful. On the first page it looked quite ordinary. It seemed to start slowly. The notes were spaced far apart. There seemed to be a kind of running, periodic left hand rhythm. The right hand seemed to start with a slow tune of some sort. Polani leafed through the other pages. It was impossible to say how it sounded. Some pages had few notes on them, while on others the stave was almost full with quavers, crochets, arpeggios, accidentals - a mass of musical notation. Both men stared hopelessly at the computer output on which every note was printed with impeccable neatness and precision.

``The first perfect sonata.'', croaked Polani, drily.

Hallam responded with a watery smile. He had never felt so nervous in his life.

There was nothing else to be said or done. Polani walked over to the piano, opened the lid and placed the music on the stand.

``Please turn the pages.'' he whispered.

The musician sat down, shifting nervously in his seat until he felt quite comfortable. The building was deserted and silent and the grounds outside were dark and still. Then, into the stillness, Polani began to play.

The opening phrase was simple but exquisite. Over the top of a gentle, rocking rhythm, a strange and exotic overture enticed the senses with a promise of greatness and beauty. Suddenly, the first theme appeared. The tune was profoundly simple, yet hypnotic and intoxicating too. It was haunting, full of emptiness almost to the point of despair. The music almost seemed desperate in its hunger, in its craving for something that was beyond the power of the listener to provide. Hallam listened in horror to the most awful loneliness he had ever felt in his life.

Then, gently at first, a second melody appeared, partly in the right hand, but more emphasised in the left. Subtle though it was, the tune carried with it the germ of hope, perhaps even warmth. The harmony between the two melodies was absolutely astonishing. Both tunes were simple yet the interaction between the two produced an overall impression that dwarfed the sum of the parts. The second tune was slowly growing in intensity, and now imparted much more than the vaguest impression of hope. But the despair of the first tune was becoming worse too, and for a moment the distance between the two melodies was nothing short of terrifying. Sometimes the tunes would clash in terrible disagreement, while at other times they would magnify each other in an even more fearful concurrence. Without warning the second melody suddenly exploded into its full glory. Suddenly the ear realised that what it had just heard from the second tune in the previous bars was nothing but the merest shadow of its true potential. The melody was now deep and glorious, magnificently warm, exuding infinite hope from every living note. The original, haunting, lonely theme could still be heard, as awful as ever, yet in some miraculous way each half of the music seemed to be singing in complete harmony with the other. At times they almost seemed to be the same tune, and when this happened, every sense gorged on the music, craving its astounding voice.

Hallam turned page after page, the hairs on the back of his neck bristling, while the pianists hands eloquently translated the meaningless symbols into the most profound music humanity could ever know. While Hallam listened, despair itself had been turned to hope, and emptiness to beauty. But only half the pages had been turned, and the music was to continue with the most remarkable twist. Suddenly both tunes erupted into a kaleidoscope of unsurpassed exuberance. For an entire four pages, the piano sang with a million voices, each one a drop in an insatiable fountain of passion and pleasure. The virtuosity was unbearable as every finger on every hand forced the cadenza to ever greater and more dangerous heights. The piece was alive like a great beast of unimaginably demanding proportions. A beast that felt neither respect nor remorse as it plundered the deepest recesses of musical expression. And yet it was impossible to abhor the crime for what it was, because in a truly exquisite moment the listener himself both belonged to and controlled that beast.

But in the next moment the piece had changed again. The original melodies suddenly re-appeared for a moment, continuing the eternal struggle of their addictive refrain. Then a second later the awful passion was back, seemingly using every single note of the piano and all those in-between. Then the tunes returned again in an insuppressible fit of variety. From nowhere, and for only the briefest moment, the chaos was joined by the vaguest hint of a fourth theme, and then, in a paroxysm of discord...there was silence.

Polani's fingers lifted completely off the keyboard, but the strings of the piano still resonated. In the following moment, the music suddenly faded and died. Hallam turned the final page. There were still notes left to play. Now Polani's fingers reared up over the keyboard once more, and in another second the music was brought back to life. This time the theme, which had appeared so briefly just a moment before, was neither fast nor slow, soft or loud, but instead filled with a most remarkable and beautiful serenity. Sometimes the music was reminiscent of that second melody, while at other times the faintest remnants of the original haunting refrain could almost be detected - yet somehow just out of reach.

The concluding bars were of the most delicate virtuosity that Hallam could hardly comprehend what Polani's own fingers were playing. The serenity was so vivid that it was like standing for the first time in the most beautiful place on earth, having only ever studied the world from an old black and white picture before. For a moment he stood on the top of the highest and most colourful mountain, with anything he cared or dared imagine sprawled out in complete humility below. In that moment, he knew beyond any doubt that their work had been a success. He was convinced he had witnessed the very voice of God.

The piano fell silent for the last time, and for a full minute nothing was said between the two men. Then Hallam put his thoughts into words.

``I don't believe it, you were right. That was the most indescribably fantastic piece of music I've ever heard in my life. That was surely the greatest of all great sonatas.''

But Polani stood up and turned to Hallam with a look of great dissatisfaction on his face.

``I'm sorry to have wasted your time, Sir. I'm afraid our experiment appears to have failed completely. I've never heard such mediocre nonsense in all my professional life.''

And with that he turned on his tiny heels, and left.