Decoded

by Mai Jia

  The very first winter after the end of the Second World War, Jan Liseiwicz went back to Europe. The weather was terribly cold, but I guess that it was even worse in Europe, because he didn’t take any of his family with him – he just went on his own. When he came back, Daddy borrowed a Ford car from the university and told me to go down to the docks to collect him. When I got there I was stunned to see that Professor Liseiwicz was sitting on an enormous wooden packing case, about the same size as a coffin, with his name and address at N University written on it in both Chinese and English. The size and the weight of his packing case made it impossible to get into the car. I had to get a cart and four brawny men to transport it back to the department. On the way, I asked Liseiwicz why on earth he had brought so many books back with him and he said excitedly, ‘I have a new research interest and I need these books!’

  Apparently on this trip to Europe, Liseiwicz had recovered the interest in research that had been dormant in recent years: he was feeling inspired and was going to make a new start. He had determined to begin research on an enormous new topic: artificial intelligence.

  Nowadays, everyone has heard of the subject, but at that time the world’s first computer had only just been built.* That was what had given him the idea – he was way ahead of most people in realizing the potentials of the field. Given the massive scope of the research project that he had in mind, the books that he brought back were just a tiny part of the whole; but it is not surprising that he was not prepared to lend them to other people.

  The problem is that the blanket ban applied to everyone except Zhendi, and so people started making wild guesses about what was going on. There were all sorts of stories circulating in the mathematics department anyway about what a genius Zhendi was – how he completed four years of study in the space of two weeks, how cold sweat broke out on Professor Liseiwicz’s face at the mere sight of him; and before you knew it, some people who didn’t understand the first thing about how these things work were saying that the foreign professor was using Zhendi’s intelligence to advance his own research.

  That kind of gossip breaks out all the time in academia – it makes professors look bad and people enjoy the idea that they get where they are by stealing someone else’s work – that is just the way it is.

  When I heard this story, I went right round to Zhendi to ask him about it and he said it was a pack of lies. Daddy asked him about it too and he still said it was all rubbish.

  Daddy said, ‘I hear that you spend every afternoon round at his house, is that right?’

  ‘Yes,’ said Zhendi.

  * The world’s first computer, ENIAC, was built in 1946.

  ‘What are you doing there?’ asked Daddy.

  ‘Sometimes I read books, sometimes we play chess,’ said Zhendi. Zhendi was very definite, but we still felt that where there is smoke, there must also be fire – we were worried that he was lying. After all, he was still only sixteen years old and knew nothing about how complicated the world can be; it was quite possible that he was being deceived. Well, I made excuses several times to go round to Liseiwicz’s house and find out what they were doing, and every time I saw that they were indeed playing chess: the standard international game. Zhendi often played go at home with my father, and he was a fine player – the two of them were pretty evenly matched. Sometimes he also played tiddlywinks with Mummy, but that was just for fun. When I saw the two of them playing chess together, I thought that Liseiwicz was just doing it to keep him company, because everyone knew that he played at grandmaster level.

  In fact, something completely different was going on. According to what Zhendi told me himself, he and Liseiwicz had played all sorts of different kinds of chess together – the standard kind, go, elephant chess, battle chess and so on. Occasionally he could win at battle chess, but he never beat Liseiwicz at any of the others. Zhendi said that Liseiwicz played all these games to an amazingly high level, so the only reason that he could occasionally win at battle chess was because ultimately victory in that game is not dependent entirely upon the player’s skill; at least half the time the outcome is determined by sheer luck. If you think about it, even though tiddlywinks is a much simpler game than battle chess, it is a much better determinant of the player’s skill, because the element of luck is so much smaller. In Zhendi’s opinion, battle chess should strictly speaking not be considered a type of chess at all; at the very least, it should not be regarded as a chess game for adults.

  You may well be wondering, given that Zhendi was so far from being able to give Liseiwicz a good game, why did they keep on playing together time after time?

  Let me explain. As a game, all types of chess are easy to learn to play, in the sense that they do not require the player to develop any special skills: you can just learn the basic rules and get stuck in. The problem is that once you have started playing, chess calls upon completely different attributes from any game requiring physical skill, where as you practice you just get better and better; from a rank beginner you become a practiced player, then a skilled one, and finally an excellent one. The more you play chess the more complicated it gets. The reason for this is that as you improve, you learn more of the set variations and that then opens up more avenues for you to explore – it is like walking into a maze. At the entrance, there is only one way to go, but the further you penetrate, the more crossroads you encounter; the more options you are faced with. That is one reason that the game is so complex; the other is that as you might imagine, if two opponents are walking through the maze at the same time, as one proceeds he is also trying to block the other’s advance, and he is trying to do the same – advance and block, advance and block – well, that is adding another level of difficulty to an already extremely complex game. That is what chess is like: you have standard openings and endgames, attacking and defensive moves, obvious and secret manoeuvres, pieces that you move close at hand and those you send to the other side of the board, enveloping your opponent in a fog of mystery. Under normal circumstances, whoever knows the most set variations has the most room to manoeuvre, and can create the most mystery about his moves. Once his opponent has become confused and can no longer determine the direction of attack, he has created the most favourable circumstances to win the game. If you wish to play a good game of chess, you have to learn the set variations, but that is not enough. The whole point about set variations is that everybody knows about them.

  What is a set variation?

  A set variation can best be compared to a path beaten through the jungle by many passing feet – on the one hand you can be sure that it is a route that goes from A to B, on the other hand it is also available for anyone to use. You can travel this path, but so can everyone else. Or to take another example: set variations are like conventional weapons. If you are fighting against people who have no weapons at all, your weapons will kill them dead in an instant. On the other hand if your opponent has exactly the same conventional weapons, you may be out there laying mines but he just sends in the minesweepers to clear them up, so you have been wasting your time; you send up your planes but he can see them bright and clear on his radar and he can blow you out of the sky. In those circumstances, you need secret weapons to win on the battlefield. Chess has many secret weapons.

  The reason that Liseiwicz was prepared to carry on playing chess with Zhendi was because he realized that he had many secret weapons. He seemed to be able to conjure up an endless series of bizarre and tricky moves, apparently from thin air, giving his opponent the feeling that as he was walking along, someone was tunnelling through the ground beneath his feet. He could really confuse you, because a piece that you thought was dead would – in his hands – suddenly turn out to be crucial for his next move. Zhendi had been playing chess for such a short time, he had so little experience, and he knew so few of the set variations that it was easy to confuse him with your conventional weapons. Or to put it another way, because he did not know any but the most basic set variations, your standard moves wer
e deeply mysterious to him. Of course each of these moves had been used by tens of thousands of people – they are reliable, they have been proved time and time again – so whatever peculiar and tricky move he had thought up was not able to stand up against the tried and tested, and in the end he would lose the game yet again.

  Liseiwicz once told me himself that Zhendi was losing not on the basis of intelligence, but on experience, knowledge of the set variations, and playing skill. Liseiwicz said, ‘I have played all sorts of different kinds of chess, starting at the age of four, and over the course of the months and years I got to learn the set variations for each type of game like the back of my hand. Of course it is difficult for Jinzhen to beat me. The fact is that there is no one in my immediate circle who can beat me at chess – I can say without fear of contradiction that at chess, I am a genius. Furthermore, having played for such a long time, I have honed my skills. Unless Zhendi were to spend the next few years concentrating solely on improving his chess-playing abilities, he is never going to be able to beat me. However, when we range our forces against each other, I often feel a refreshing sense of surprise, which I enjoy enormously – that is why I have carried on playing with him.’

  That is what he said.

  Another game of chess!

  And another game of chess!

  Because they were playing chess together, Zhendi and Liseiwicz became close friends – they quickly moved beyond the normal teacher–pupil relationship to become really good friends, going out for walks together and eating together. Because they were playing chess, Zhendi spent less and less time at home. Up until then, during the summer and winter holidays, Zhendi would hardly put his nose out of doors – Mummy would often have to practically throw him out of the house in order to get him to spend some time in the fresh air. However, that winter Zhendi was hardly ever at home during the day; to begin with we thought he was playing chess with Liseiwicz but later on we found out that this was not the case. They weren’t playing chess – they were developing a new kind of board game.

  I am sure that you will find it difficult to believe they were inventing their own variant of chess – Zhendi called it ‘mathematical chess’. Later on, I got to see them play on many occasions and it was really weird – the board was about the same size as a desktop, and there were two military encampments on it – one was a kind of hatch # shape, the other the shape of a Coptic cross. They played this game with mahjong tiles rather than chess pieces. There were four routes across the board and each player held two of them, stretching out from the hatch and the Coptic cross encampments. The pieces that started in the hatch encampment had a set arrangement, somewhat like that seen in elephant chess, where each piece has a particular starting position, but the pieces in the Coptic cross encampment could begin in any position – the arrangement was determined by your opponent. When your opponent arranged your pieces, he was of course thinking entirely of his own plan of campaign, placing them in the most favourable positions for his own purposes. Once the game began, you took over control of these pieces and it was up to you to move them. Naturally, your priority was to move these pieces from a position advantageous to the enemy to one favourable to yourself at the earliest possible opportunity. During the course of a game, a piece could move between the hatch and the Coptic cross encampments, and in principle, the fewer impediments you faced in advancing your pieces into the enemy encampment, the greater your chances of victory. However, the rules governing the circumstances in which you could simultaneously move a piece into the opposition camp were very strict and needed careful planning and preparation. Furthermore, once a piece had entered the enemy encampment, the way in which it could move changed. The biggest difference in the types of movement possible was that pieces in the hatch encampment could not move on the diagonal nor could they jump over other pieces. Both of these types of moves were allowed in the Coptic cross encampment. Compared to standard chess, the biggest difference was that when you were playing, you had to be thinking about how you would advance your own pieces along the two routes under your control: making sure that you had them arranged for the moves you intended to carry out, while at the same time making sure that at the earliest possible moment the disadvantageous pieces were moved into better positions and that when the time came, both you and your opponent could simultaneously move a piece into the enemy camp. You could say that you were playing chess against your opponent, but also against yourself – it felt as though you were playing against two different opponents at one and the same time. It was one game, but it was also three, for each of the two players had the game going on against themselves, as well as the one against their opponent.

  It was a very complicated, strange game. The best comparison I can think of is to say that it is like the two of us joining battle, only to discover that my troops are under your command and your troops are under my command. Just think how bizarre and complicated it would be to fight a battle with only the opposing army at your command – bizarreness can in some cases be a kind of complexity. Because this game was so very complicated, most people simply could not play it. Liseiwicz said that it was designed solely for mathematicians to play and that is why it was called mathematical chess. There was one occasion when Liseiwicz was chatting to me about this game and he said triumphantly: ‘This game is the result of much research into pure mathematics: given the level of mathematical knowledge required to deal with its complexities, not to mention its intricate rules, the subtle way in which the subjective role of the player transforms the structural organization – really only human intelligence can compare. Inventing this chess game was a way of challenging the limits of our intelligence.’

  The minute he said this, I was immediately reminded of his current research topic – artificial intelligence. I suddenly felt alarmed and uncomfortable, because I started to wonder whether this mathematical chess might not be part and parcel of his research. If that was the case, then Zhendi was clearly being used – he was covering up what he was doing by pretending that it was all about developing this game. I then made a special point of asking Zhendi why they had decided to develop mathematical chess and how they had gone about it.

  Zhendi said that they had both enjoyed playing chess together but that Liseiwicz was so strong a player that he simply had no hope of ever being able to beat him, which in turn made him depressed and unwilling to play. Afterwards the pair had started thinking about developing a new kind of chess game, whereby the two of them would both start at the same level, without one having the advantage of knowing all the set variations. This game was to be structured so that victory would be determined purely by intelligence. When they were designing the game, Zhendi said that he was primarily responsible for designing the board, while Liseiwicz worked out the rules for how the pieces would be allowed to move. In Zhendi’s opinion, if you wanted him to work out how much of the game was his own work, he would say that it was around 10 per cent. If this game was indeed part of Liseiwicz’s research, then Zhendi had made a significant contribution and he deserved some credit for it. So I asked about Liseiwicz’s work on artificial intelligence. Zhendi said that he knew nothing about it and that so far as he was aware, Liseiwicz was not working on anything of the kind.

  I asked him, ‘Why do you think that he is not working on anything of the kind?’

  Zhendi said, ‘He has never mentioned it to me.’

  It was all most strange.

  I thought to myself, the moment Liseiwicz caught sight of me he was bubbling over with news of this new research plan, but now Zhendi spends pretty much every day with him and he doesn’t say a word about it? I was sure that something was up here. Later on, I asked Liseiwicz about it myself, and the only reply was that we did not have the facilities, he could not continue, and so he gave up.

  Gave up?

  Had he really given up or was this just something that he was saying?

  To tell the truth, I was very unhappy about the whole thing. I don’t need to tell you, if h
e was just pretending to have given up on this research then we had a serious problem, because only someone who is engaged in unethical (if not downright criminal) activities feels the need to hide from other people’s eyes like that. The way that I thought about it, if Liseiwicz was indeed involved in something unethical, there was only one person he could be using, and that was poor little Zhendi. The whole department was buzzing with rumours, which had already forced me to think seriously about the unusual relationship that had developed between Liseiwicz and Zhendi – I was really worried that he was being cheated, being used. He was really still only a child at the time, completely unaware of how nasty other people can be, very emotionally immature and naïve. If someone is looking for a patsy, that is the kind of person that they would pick: innocent, isolated, timorous; the kind of person where if you bully them they keep quiet about it; the kind that suffers in silence.

  Fortunately it was not long after this that Liseiwicz did something truly unexpected, which completely put all my fears to rest.

  [To be continued]

  8.

  Jan Liseiwicz and Jinzhen finalized the rules for mathematical chess in the spring of 1949. Not long afterwards, which was also not long before the provincial capital, C City, was liberated, Liseiwicz received an invitation from the journal, the Annals of Mathematics, to attend an event to be held at UCLA. In order to facilitate the travel arrangements for attendees from Asia there was a contact address in Hong Kong. Everyone was to meet there and then fly to California on the final leg of their journey. Liseiwicz did not spend very long in the States, maybe a month and a half in total, and he was back at work at the university so quickly that people found it hard to believe that he could really have been to America and back in that time. However, he had plenty of proof: job offers from universities and research institutions in Poland, Austria and the US; photographs of himself in the company of John von Neumann, Lloyd Shapley, Irvin Cohen and other famous mathematicians. In addition, he had brought back the question paper for that year’s Putnam Mathematical Competition.