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 controclass="underline" 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 he 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.