## The Mutilated Chess Board

We have a chessboard with the two opposing corners removed,so that there are only 62 squares remaining.Now we take 31 dominoes shaped such that each domino covers exactly two squares. The question is:is it possible to arrange the 31 dominoes so that they cover all 62 squares on the chessboard?

There are two approaches to the problem:
(1) The scientific approach
The scientist would try to solve the problem by experimenting,and after trying out a few dozen arrangements would discover that they all fail.Eventually the scientist believes that there is enough evidence to say that the board cannot be covered.However,the scientist can never be sure that this is truly the case because there might be some arrangement which has not been tried which might do the trick.There are millions of different arrangements and it is only possible to explore a small fraction of them.The conclusion that the task is impossible is a theory based on experiment,but the scientist will have to live with the prospect that one day the theory may be overturned.
(2) The mathematical approach
The mathematician tries to answer the question by developing a logical argument which will derive a conclusion which is undoubtedly correct and which will remain unchallenged forever.One such argument is the following:
* The corners which were removed from the chessboard were both white.Therefore there are now 32 black squares and only 30 white squares.
* Each domino covers two neighbouring squares,and neighbouring squares are always different in colour,ie one black and one white.
* Therefore,no matter how they are arranged,the first 30 dominoes laid on the board,must cover 30 white squares and 30 black squares.
*Consequently,this will always leave you with one domino and two black squares remaining.
*But remember all dominoes cover two neighbouring squares,and neighbouring squares are opposite in colour.However,the two squares remaining are the same colour and so they cannot both be covered by the one remaining domino.Therefore,covering the board is impossible!

"Fermat's Last Theorem" by Simon Singh (p24)

Exile to Hell  Isaac Asimov

He considered the chessboard carefully and his hand hesitated briefly over the bishop.
Parkinson,at the other side of the chessboard,watched the pattern of the pieces absently.Chess was,of course the professional game of computer programmers,but under the circumstances,he lacked enthusiasm. By rights,he felt with some annoyance,Dowling should have been even worse off; he was programming the prosecution's case.

Climatic Chess
The game of chess involves a number of pieces and a board ruled into squares. Moves in the game take place at discrete time intervals, according to the laws of the game. Numerical weather-prediction is like a huge game of three - dimensional chess. Imagine a fine grid of points drawn on the surface of the Earth, at several heights to track the up - down motion of the atmosphere as well as north-south and east west. This is the chessboard. The weather now is described by assigning, to each grid point, several numerical values: pressure, temperature, humidity, wind-speed. These are the chess-pieces. The weather tomorrow also corresponds to a position in the game but the disposition of the pieces is different. "Cyclone to Queen's Knight743." " Blizzard to King's Lynn, Showers with Sunny Intervals to Bishop's Stortford." We can measure today's weather using meteorological stations, ships, weather- balloons, and satellite pictures. So we know how to set up the pieces. The main question is, what are the rules of the game? The rules are the equations of motion of the atmosphere. As we saw, these were found centuries ago by the likes of Leonhard Euler and Daniel Bernoulli. By letting time flow in tiny discrete steps, say one second long, the equations can be viewed as rules telling us how to get from the position now to the position in one second's time. Predicting the weather one second ahead may not sound a practical contribution to the weighty problems of human kind, but that's just one move in the game. Repeat the calculation, and you have the weather two seconds into the future. After 86,400 iterations, you'll know the weather a day from now. After 8,640,000 you'll know the weather a hundred days from now. After 8,640,000,000 . . . And in essence that's how it's done. Thousands upon thousands of repetitive calculations based on explicit and deterministic rules.Just what the computer is good at.

Twixt Zero and Infinity
There's a philosophical curiosity involved in all this. The atmosphere isn't really a perfectly divisible continuum; it's a lot of fairly solid little atoms charging around like lunatics crashing into each other. The equations of smooth ideal classical mechanics replace this discrete physical reality by a fluid. But in order to solve those equations we approximate them by something discrete again. We let time click ahead in tiny steps,continuously, and we divide space up into a fine grid. This is forced by the structure of computers: they can only do arithmetic to some definite number of decimal places, say ten, in which case everything is an integer multiple of 0.0000000001. To represent an infinite decimal exactly requires an infinite amount of computer memory, which isn't feasible. The philosophical point is that the discrete computer model we end up with is not the same as the discrete model given by atomic physics. But there's a very practical reason for this: the number of variables involved in the atomic model is far too large for a computer to handle. It can't track each individual atom of the atmosphere. Computers can work with a small number of particles. Continuum mechanics can work with infinitely many. Zero or infinity. Mother Nature slips neatly into the gap between the two. So we do the best we can. Mathematicians hope that this double approximation provides answers that are close to the real thing. There are no substantial theoretical proofs that this is so; but there's compelling evidence that it works. Until some genius develops new theoretical tools, we accept the miracle and plough ahead regardless. It is, however, worth remembering that when you "put the problem on the computer" you do nothing of the kind: you represent some idealization of the problem in the computer. This is one reason why the computer cannot be a universal palliative for the ills of science and society. It just isn't clever enough yet.

"Does God Play Dice?" Ian Stewart (p116)

Falsifiability
In science,there's a time honoured way to find out whether a theory is right. Experiment.
More accurately,an experiment can tell you whether a theory is wrong,for you can never be absolutely certain that it's right.You can prove a theorem in mathematics,but you can't prove a theory. As the philosopher Karl Popper emphasized,testing a scientific theory is a matter of falsification,not verification.
The more a theory fails to be falsified when confronted by experiment,the more likely it is to be true;or at least the broader the range of conditions under which it works.But you can never be certain the theory is absolutely correct,even if it survives a million experimental tests;for -who knows? -it may fail at the million and first.

To count as scientific,a theory must in principle be falsifiable.On the island of Corfu,there's a superstition that if you see a praying mantis,it either brings you good luck - or bad luck,depending on what happens.This belief doesn't amount to a scientific theory;not because you can't measure "luck",but because it's hard to see how an experiment could disprove the theory even if you could.
None of this means that the inhabitants of Corfu are wrong. What we're discussing is the limits on scientific knowledge. There may be true things in the universe that cannot be known in the scientific sense.However,it's going to be hard to resolve disputes about them.

"Does God Play Dice?" Ian Stewart (p164)

[Upon this basis,belief in God or any other superstition is rather like belief in the capacity of a praying mantis to provide good or bad luck.The idea is somewhat tautological,the luck will happen anyway,regardless of a praying mantis being behind it,and so the mantis is nothing to do with the cause and effect.
Evolution has been around for ages and has withstood every stone thrown at it,thus increasing the likelihood that it is right.Every attempt at falsifying it has failed.Evolution wasn't assumed to be true in the first instance,it has grown to be more likely to be true over time.Belief in God or any other mysticism assumes the truth of the statement in the first instance,and claims it as the truth until such time as counter-evidence is found.This inverts the scientific scenario of how a theory builds it's reputation.Mystics assume the reputation of their belief first and then have to have it denied.

Bizarrely the likes of Russell Stannard attempt to perform experiments on beliefs in God to try to assert their validity,at least he is trying to use the scientific method the right way around.Mystics assume cause and effect with no proof, rather as the inhabitants of Corfu do with mantis,and even if counter evidence or lack of evidence undermines that position,they hold onto it anyway,regardless of whether it is valid.As Ian Stewart suggests in his book,there could very well be an invisible monster creating the observed chaos in the universe,but we have no evidence for such a creature,and any theory of invisible monsters would have to hold it's own over time and prove itself as one attempted to falsify it,assuming that it was,in principle falsifiable.
By comparison,mystics would assume that an invisible monster was there,and performed actions in the world,with no evidence to show that a monster was indeed the cause,and when the monster theory was falsified,would still adhere to that theory even though it was wrong,or as with the people of Corfu at least be in the position of not being able to be proved correct,and are thus just as likely to be incorrect.Likewise with God and other beliefs,one cannot show either conclusive evidence for or against,and thus there is no reason to believe with great conviction something which has so little credence.

Even if one had a "theory of God",such a theory would have to stand the same sort of scrutiny that a scientific theory does.As with Russell Stannard one is forced into a farcical scenario of second guessing God and what things an omnipotent deity will or won't do or be capable of,or assuming that such a being will be at your beckoning.Whichever way you look at it, unsubstantiated belief is a farce,you just can't win. You can't prove anything, and you can't prove anything wrong. Thus there is just no point in doing it. Notwithstanding the plethora of evidence in Nature of adaptation and change which shows that evolution is going on,denying that it is makes no sense,if one is doing it purely on the basis of a convicted belief.As Ian says,such things as evolution are "theories" and as such cannot be 100% true,so any such theory cannot represent a direct assault on a convicted belief by being "proved correct".
The view that seeks to keep evolution out of the classroom is thus misinformed about the nature of a scientific theory.It is not a threat to a convicted belief. Any sane person though,would actually think that any premise would need evidence to support it and have cause and effect shown.This is not done in the case of superstitious belief.
For the above reason,belief in God cannot be proved true or false,whereas a theory such as evolution can show itself to have pertinence as time goes on,so if they are to be taught alongside each other,if anything evolution has a greater claim to be taught,since at least it has evidence to support it,whereas belief in "invisible monsters" does not,and can't have any positive evidence that it is true. -LB]

## The King makes his move.....

Did you ever here the story of the King that required the help of a mathematician? Having performed a service for the King,the mathematician was asked how he could be rewarded.He asked that the King place a grain of rice on the first square of a chess board,and double the number of grains thereafter on each subsequent square.The King thinking this was a trivial reward asked whether this was all the mathematician wished of him.This was all the mathematician wished and so the King went ahead,placing grain after grain on the board,each square having double the number of grains in the previous one.

 Starting at square one,and doubling,numbers grow exponentially fast.On reaching the 28th square there would be 2.7x108 elements.On the 64th square there would be 1.8x1019 elements.

It soon became apparent to the King that he had been asked for a larger reward than he had first supposed, for the number of grains quickly mounted,until the board could no longer contain them.
Have you ever heard of Moore's Law? The premise that the number of transistors on a computer chip will double in 18 months? The number of transistors on current processors would require a number that inhabits the 28th square of the chess board,using the King's grains to measure it,after this point there becomes a physical limit on the number and size of the transistors. In order to continue the size of the transistor becomes comparable with wavelengths of light,and the signal is no longer capable of sticking in the transistor that holds it. It's possible that because of this such circuits will exhibit "quantum interference effects" which may or may not be beneficial depending on how they are exploited.
The King's move is one square at a time.Perhaps if he had conceived of the board all at once,he would not have found himself at a disadvantage with numbers.It seems that a quantum computer will have the advantage of the King.

 A SHORTCUT THROUGH TIME: THE PATH TO THE QUANTUM COMPUTER by George Johnson In the 1960s Gordon Moore made the empirical observation that the density of components on a chip was doubling roughly every 18 months. Over the past 40 years, Moore's law has continued to hold. These doublings in chip density explain why today's personal computers are as powerful as those that only governments and large corporations possessed just a couple decades ago. But in 10 to 20 years each transistor will have shrunk to atomic size, and Moore's law, which is based on current silicon technology, is expected to end. This prospect drives the search for entirely new technologies, and one major candidate is a quantum computer--that is, a computer based on the principles of quantum mechanics. There is another motive for studying quantum computers. The functioning of such a device, which lies at the intersection of quantum mechanics, computer science and mathematics, has aroused great intellectual curiosity. Buy it Now! What is Moore's Law? [Video] Ever wonder why Apple puts out a newer, tinier iPod every two freaking seconds? Or why you're watching this on a laptop instead of a blinking, blooping Star-Trek-style wallputer? Moore's Law is the reason. Christie Nicholson explains how it works -- in pretty much the lowest-tech way possible.

## ....and the Queen makes hers

This is where the gods play games with the lives of men, on a board which is at one and the same time a simple playing area and the whole world. And Fate always wins. Fate always wins. Most of the gods throw dice but Fate plays chess, and you don't find out until too late that he's been using two queens all along. Fate wins. At least, so it is claimed. Whatever happens, they say afterwards, it must have been Fate.* Gods can take any form, but the one aspect of themselves they cannot change is their eyes, which show their nature. The eyes of Fate are hardly eyes at all - just dark holes into an infinity speckled with what may be stars or, there again, may be other things. He blinked them, smiled at his fellow players in the smug way winners do just before they become winners, and said: "I accuse the High Priest of the Green Robe in the library with the double-handed axe." And he won. He beamed at them.

*People are always a little confused about this, as they are in the case of miracles. When someone is saved from certain death by a strange concatenation of circumstances, they say that's a miracle. But of course if someone is killed by a freak chain of events - the oil spilled just there, the safety fence broken just there - that must also be a miracle. Just because it's not nice doesn't mean it's not miraculous . - Terry Pratchett "Interesting Times"

## Chess masters pit wits and pride to stop machine becoming champion

A computer is contesting a national chess championship for the first time,reports David Harrison in Rotterdam

 Every move you make:grand master Frisco Nijboer plays Fritz,the computer."The essence of competition at this level is man versus man," say sceptics

Frisco Nijboer the Dutch grand master, slid the white king's pawn forward, took a sip of water and looked up at his opponent. It was a conditioned reflex. Nijboer was playing Fritz the computer and Fritz, competing in the Dutch national championships, was not about to give anything away through body language.

 Frans Morsch,the program's creator

The creator of Fritz's program, Frans Morsch, a Dutchman, input the coordinates of Nijboer's move on a keyboard. Within seconds the computer delivered its response. Nijboer had barely time to put his glass down. A black pawn moved forward to block his white adversary.
The move was relayed simultaneously on Fritz's screen and a television monitor watched by the audience. Morsch then duplicated Fritz's move on the chessboard in front of Nijboer and sat back to wait.
Fritz is the first computer ever allowed to compete in a national championship and the move has appalled traditionalists and many of the world's leading players, including Britain's Nigel Short, a former world championship finalist.
They argue that national tournaments are about man versus man, not man versus machine. And they are horrified by the prospect of a computer being the chess champion of the Netherlands, one of the stronger chess-playing nations - by Friday night Fritz was joint second with six games to play.
The games are being played on six tables on the stage of Rotterdam's Library Theatre. Five tables have two human competitors each. The one on the left has Nijboer and the computer.
An audience of about 40 looks on, copying the players' monastic silence and following every move on six screens. The auditorium is dimly lit but spotlights beam on to the tables.
Fritz's presence has altered the mood of the tournament. Another grand master, Paul van der Sterren, has boycotted it, while Manuel Bosboom resigned in protest after four moves of his game against Fritz. Computers don't belong here," he said. They are ugly and absurd."
Others are playing on and, despite the complaints, are curious about their electronic rival. When they rise for a break most drift towards Fritz's table to check proceedings. The computer was named by its German marketing company. The blurb refers to Fritz having been "born in Hamburg in November 1991" and lists its parents as Morsch, Matthias Feist and Matthias Wüllenweber.
The computer terminal is only the top half of Fritz. The rest is hidden below the stage. The package includes four powerful processors containing a huge database on all the participants in the championships, along with a large store of game openings and endgame strategies.
The speed of its responses can be demoralising. The talented Jeroen Piket, 31, who has twice beaten Garry Kasparov and drew with Fritz last week, said: "I'd spend 15 minutes deciding on a move, then he'd reply in a few seconds. It's a bit shocking."
The players accept that computers have an important role to play in helping people learn the game and prepare for matches. But they say machines have unfair advantages in top-level tournaments.
Fritz has a record of all the moves played by his opponents in their previous matches, enabling him to work out how they are likely to respond to his moves. The human players can study opponents' past strategies before a game but not during it.
There are other crucial factors. Fritz never tires, his mood is never affected by a bad night's sleep or a row with his wife and he is impervious to psychological warfare.
The Dutch Chess federation is backing Fritz. A spokesman said the computer had generated interest in chess and increased the prize money by £19,500, to £43,750.
Morsch said it was "absolutely right" to pit him against humans. Five years ago they couldn't do it and in another five years they will be too fast for humans. Now is the time when it makes for interesting matches."
But Nigel Short, a world championship finalist against Garry Kasparov in 1993, said: "The Dutch Chess Federation must have gone completely nuts. You wouldn't let power boat compete in a swimming event or a forklift truck in a weight lifting competition."
Fritz's enemies have at least one consolation: if he wins will not be allowed to take home the prize money.

The Sunday Telegraph 14 May 2000

## Shobna's chess challenge

Street star joins the Kirsty fundraiser
CORONATION Street star Shobna Gulati checked in to help the £5m appeal for the future of Didsbury's children's hospice. Shobna, who is shop girl Sunita Parekh in the Granada television soap, sat down with chess grandmaster Jonathan Rowson as he tried to break the British record for games played simultaneously.
Jonathan played 150 games in nine hours, winning 137, drawing 12 and losing one. The record stood at 142, set in December 1956. The record holder Jeff Martin flew in from America to witness the attempt to steal his crown.
Players taking part in the event, organised by Mind Sports Olympiad, a nine day festival of thinking games and mental skills, included total novices to grand-masters from Greater Manchester .
All money raised from the games, played on 150 tables at the Sugden Sports Centre, Grosvenor Street, Manchester will be donated to help safeguard the future of the Francis House Children's Hospice in Didsbury.
Kirsty Howard, who fronts the appeal that has reached £2.25m, has been feted by celebrities for the way she has ignored her own health problems to work for the appeal.
Kirsty, who was born with her heart back to front, stomach problems and some organs, including her liver, in the wrong place, was not able to attend.Susie Mathis, co-ordinator of the hospice campaign, said: "It never ceases to amaze me the different areas of support the appeal receives, and each one is as important as the next. "It really doesn't matter whether it is a chess championship, sponsored head-shave, military two-step or cheerleaders doing the bit to raise money, every penny counts and is much appreciated." Susie, who is helping to prepare a glitzy, star-studded fund-raising ball in time for Kirsty's eighth birthday on September20, added: "Healthwise, Kirsty is about the same, but her spirit just gets brighter and brighter.
She is an amazing little girl, and as we approach half-way in the £5m appeal to secure the future of Francis House, I hope we can get through the second half of the fund-raising even quicker" David Levy, event founder of Mind Sports Olympiad, said: "We wanted to organise a special curtain-raiser for the Olympiad, to thank Manchester for supporting our event. It is hard to think of a more worthwhile cause."

## The clockwork grandmaster

 It astonished the viennese court, impressed Napolean and Edgar Allen Poe,and for decades proved a match for the world's leading chess players. But what was "The Turk"? A machine? A man? Or something in between? In this extract from his new book,Tom Standage pieces together the story. A chequered career "In Paris,The Turk defeated Benjamin Franklin;and though it lost to François-André Danican Philidor,the best chess-player in Europe,the match was a public relations triumph".

In the spring of 1770, an extraordinary mechanical man known as "The Turk" made his debut at the imperial court in Vienna. He was fashioned from wood, powered by clockwork and dressed in a stylish Turkish costume. His inventor, a 35-year-old Hungarian civil servant by the name of Wolfgang von Kempelen, boasted that The Turk could beat anyone at chess, an incredible proposition in an era long before the advent of computers. Kempelen had no plans for his chess-playing machine other than to amuse the court. He could have no idea that his automaton would achieve fame throughout Europe and America, that figures such as Napoleon Bonaparte and Edgar Allan Poe would become fascinated by it, and that the mystery of how The Turk worked would remain unsolved for almost 90 years.
 Wolfgang von Kempelen Inventor of The Turk

When the Empress Maria Theresa indicated, at The Turk's inaugural appearance, that Kempelen should begin, he wheeled his automaton forward. The life-size figure sat behind a wooden cabinet or counter three feet high, four feet wide and two-and-a-half feet deep, with a board screwed to its top. The whole contraption ran on four brass castors that not only let it move freely, but also raised it slightly off the floor so that the audience could see that there was nothing untoward going on beneath.
In the style of a magician, Kempelen proceeded to put on a theatrical performance that would continue to amaze audiences for decades to come. He first opened a door on the left of the cabinet to show an elaborate mechanism of densely packed wheels, cogs, levers and clockwork machinery. Opening a corresponding door at the back, he held up a candle which was just visible through the machinery to the audience in front. He then shut these doors and opened two larger ones, revealing the other two-thirds of the cabinet. It was largely empty apart from a few metal wheels and cylinders, and two horizontal structures resembling quadrants. Again, the audience could see right through.
Kempelen closed the doors, turned a large key in the cabinet to wind up a clockwork mechanism, and the mechanical Turk sprang into life, reaching out with its left arm to move forward one of the chess pieces. Every 10 or 12 moves, Kempelen wound the key again - but apart from this he did not touch The Turk, who swiftly proceeded to defeat a number of courtiers.
The Turk's sensational performance astonished and delighted the Empress and became the talk of Vienna. By the beginning of 1783 Kempelen was ready to take his invention on tour. In Paris, it played and won against Benjamin Franklin, the American statesman and scientist, who was a chess fanatic. It also played against François André Danican Philidor, the best chess-player in Europe, and although The Turk lost, the match was a public relations triumph.
The Turk's next stop was London. It is difficult to imagine an attraction more likely to appeal to Londoners of 1783, for the city was not only a great centre for chess, but was also renowned for its enthusiasm for public displays of technical marvels. When The Turk went on show in Savile Row, the people flocked to see it, even at the considerable sum of five shillings each.
Not everyone was impressed. Philip Thicknesse, a wealthy gentleman, was absolutely certain that The Turk was a trick, because it was able to respond to its opponent's moves. Thicknesse published a pamphlet in which he declared that the real mover is concealed in the Counter". The operator could see what moves his opponents made, Thicknesse suggested, using a mirror attached to the ceiling.
A year later, Kempelen returned to Vienna, packed The Turk away into wooden crates and turned his attention to his other inventions -including an ambitious attempt to build a machine capable of imitating the human voice. In 1804 he died, and thereafter The Turk was sold to an engineer and musician by the name of Johann Nepomuk Maelzel, who was keen to make money from displaying Kempelen's automaton in public.
The Turk's most famous encounter during this period came in 1809, when it was shown to Napoleon Bonaparte. Napoleon's valet, Louis-Constant Wairy, wrote: "His Majesty took a chair, and sitting down opposite the automaton, said, laughing: 'Come on, comrade, here's to us two.' The automaton saluted and made a sign with the hand to the Emperor, as if to make him begin... The game opened, the Emperor made two or three moves, and then intentionally a false one. The automaton bowed, took up the piece and put it back in its place. His Majesty cheated a second time; the automaton saluted again, but confiscated the piece. 'That's right,' said His Majesty, and cheated a third time. Then the automaton shook its head, and passing its hand over the chessboard, upset the whole game. The Emperor complimented the mechanician highly."
It was in London in 1819 that The Turk encountered its most cunning and perspicacious observer yet: a young man named Robert Willis. Willis, like many others before him, was convinced that The Turk was controlled by a hidden operator. However, he emphasised that he did not wish to detract from "the real merits of Mr Kempelen", adding that "a more than ordinary share of skill and ingenuity must have fallen to his lot, who could imagine and execute such a machine". Willis saw The Turk as a mechanical puzzle to be solved, rather than as a fraud to be uncovered.

 The mystery explained The Turk's operator, a skilled chess player,hid by moving his sliding seat and opening or closing various partitions.

The basis of Willis's argument was the notion that no mechanism, however complex, could play chess: such a feat was, he declared, "the province of intellect alone". Yet just as Willis's pamphlet appeared, another young Englishman was coming to exactly the opposite conclusion: the computing pioneer Charles Babbage.
Babbage first saw The Turk play in London in the spring of 1819. The following year, he challenged it to a game. "Played with the 'automaton," he wrote. "Automaton won in about an hour. He played "very cautiously - a trap door in the floor of the room was very evident just behind the figure."
Babbage was certain the automaton was under human control, though he was not sure quite how. But he started to wonder whether a genuine chess-playing machine could, in fact, be built. In particular Babbage argued in his memoirs that a suitably powerful mechanical engine would be able to play games of skill such as noughts and crosses, draughts and even chess. He even sketched out a primitive algorithm or computer program, for playing board games with moveable pieces. His insights would lie at the heart of the development of computers in the 20th century, culminating in Deep Blue, the chess-playing supercomputer that is capable of analysing 200 million positions every second, and which beat Garry Kasparov in 1997.
The Turk's appearances in London between 1818 and 1821 continued to inspire discussion about the possibility of machine intelligence, with Babbage arguing that a machine capable of performing logical calculations was theoretically possible, while Willis stated categorically that it was not. But Willis had not landed the knockout punch he had hoped to deliver, and his "explanation" of how The Turk worked did little to undermine its popularity.
It wasn't until 1827 that Maelzel's game appeared to be up. An article in the Federal Gazette, an American newspaper, gave an account of two boys who claimed that they had climbed onto the roof of a shed next to Maelzel's current exhibition hall, and had seen him opening the top of The Turk's cabinet, and that a man had climbed out. Maelzel brushed off this suggestion, and later that month the Gazette stepped back from its original report.
Only in January 1857 did a truly authoritative account of how The Turk worked finally appear. It was written by Silas Weir Mitchell, whose father had bought the machine almost 20 years earlier to satisfy his own curiosity about how it operated. The Turk was indeed controlled by an operator concealed inside the cabinet. The clockwork machinery visible on its left-hand side extended only a third of the way along, so that the operator could sit behind it When the exhibitor opened the door to show the machinery, the operator slid forward to the other end of the cabinet, pulling dummy machinery into position with a string.
After the demonstration had finished, the operator could make himself comfortable and get ready to play. By the light of a small candle - the smoke was carried up a chimney-ike pipe to an aperture in the top of The Turk's turban -the operator fixed a chessboard in front of him. He then grasped a metal pointer which could be moved to point at any square on the internal chessboard. The pointer was connected to The Turk's arm via a system of levers called a pantograph, which could be used to position The Turk's arm with great precision. Whenever the pointer was positioned over a particular square, The Turk's hand would be positioned over the corresponding square of the external chessboard. The pointer could also be moved up and down, which caused The Turk to raise and lower its hand. And by twisting the end of the pointer, the fingers of The Turk's gloved left hand could be opened and closed. Each time he made a move, the operator moved the appropriate piece on his internal chessboard,and then directed The Turk's arm to move the corresponding piece on the external board.
But how could the operator tell how his opponent had moved? The chessmen on the external board contained small but powerful magnets; and just under each square of the board was a small metal disc, suspended on a delicate - coiled wire. When a chessman was put down on a particular square, the disc underneath was attracted by the magnet hidden inside the chessman, and moved upwards to make contact with the underside, of the board. When the chessman was picked up, the disc fell away and wobbled for a few seconds, on its coiled wire. By watching the underside of the board, first for a descending and wobbling disc, and then for a disc suddenly moving upwards, the operator could work out which chessman had been moved on the external board. He could then make the corresponding move on his own board, and start considering his response.
It seems likely that Kempelen used a series of operators, although their identities are unknown. In 1774, for example, Kempelen claimed that the automaton had been damaged on the way to a performance and that he would need a week or two to fix it. He also admitted that it had played very badly Presumably The Turk's operator at the time was not a strong player, and Kempelen wanted to buy time in which to find and train someone better. He was dearly able to engage a strong player for The Turk's subsequent European tour, since the automaton took on some of the finest players in Europe and lost only to the very best.
The first of The Turk's operators whose name is known was Johann Allgaier, a Viennese chess master who operated the automaton on Maelzel's behalf. Another Maelzel operator was a French player, Boncourt, who on several occasions almost let the cat out of the bag by sneezing during a game. This prompted Maelzel to install a noisy spring, to cover up any future coughs and sneezes.
After Maelzel's death in 1838, The Turk passed to Dr John Kearsley Mitchell (whose son, Silas, later revealed how it worked). Mitchell was an associate of the writer Edgar Allen Poe, who had seen The Turk three years previously and had written an article suggesting that it had a hidden operator. Mitchell was eager to know whether Poe had guessed correctly and raised the substantial sum of \$400 to find out for himself. He then set up a club for afficionados, but soon discovered that interest waned once the mystery was explained, and decided to sell the automaton to the Chinese Museum in Philadelphia. Fourteen years later, there was a fire at the Chinese Museum. Silas Weir Mitchell arrived just too late to save The Turk from destruction. It is said that, amid the fire's crackling wood and shattering glass, he fancied he heard The Turk's last words - "Echec!Echec!" - as it was engulfed by the flames.

• The Mechanical Turk: The true story of the chess-playing machine that fooled the world by Tom Standage (Allen Lane) is available for £11.90 plus £1.99 p&p from Telegraph Books Direct, 0570 155 7222

 Further Reading Does God Play Dice?  Ian Stewart Fermat's Last Theorem  Simon Singh Interesting Times  Terry Pratchett

 Chaos Quantum Logic Cosmos Conscious Belief Elect. Art Chem. Maths

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