by Mai Jia
One day, Zhendi forgot to lock the door of the lavatory and I walked in, not realizing that it was already occupied. That really wasn’t acceptable. As far as I was concerned, that was the last straw and now I wanted him out of our house. I told Mummy and Daddy that I couldn’t stand it any longer and I wanted him to start boarding at school. I told them that even though he was a relative, that was no reason for him to be living in our home and that lots of other boys lived as boarders at the school. Daddy didn’t say a word – he let Mummy do the talking. Mummy said that it wouldn’t be right to make him leave when he had only just arrived; she said that once term had started, then it might be all right for him to become a boarder.
Daddy then chipped in and said, ‘Okay, once term has started he can stay at school as a boarder.’
Mummy said, ‘We will go and fetch him so that he can spend every weekend here, because he ought to feel that this is still his home.’ Daddy agreed to that. So everything was decided.
However, that is not at all what happened in the end . . . [To be continued]
One evening, towards the end of the summer holidays, Master Rong happened to mention at the dinner table something that she had read in the newspapers earlier that day: the previous summer many parts of the country had suffered one of the worst droughts since records began, with the result that in some cities there were more beggars than there were troops. Her mother sighed and said that the previous year had been a double leap year – those years always saw terrible natural disasters. In the final analysis it was always the peasants that suffered the most. Jinzhen did not often open his mouth and so Mrs Lillie always did her best to bring him into the conversation. It was for this reason that she made a point of asking him if he knew what a double leap year was. When he shook his head, Mrs Lillie explained that it came about when a leap year in the solar calendar coincided with one in the lunar calendar; when the two leap years came together. Seeing that he didn’t really understand what she was talking about, Mrs Lillie asked him, ‘Do you know what a leap year is?’
He shook his head again, without making a sound. He was that sort of person: if it was possible to express something by any other means, he would not open his mouth. Immediately Mrs Lillie began to explain to him what a leap year was and how it was dealt with in first the solar calendar and then the lunar calendar, and so on and so forth. When she had finished, he just stared at Young Lillie as if he had been pole-axed, waiting for him to confirm what his wife had just said.
Young Lillie said, ‘Exactly. That is how it works.’
‘You mean my calculations were wrong?’ Jinzhen went bright red in the face and looked as if he was about to burst into tears.
‘Your calculations?’ Young Lillie did not know what he was talking about.
‘Daddy’s age – I thought that every year was 365 days long.’
‘That is not quite right . . . ’ Before Young Lillie had finished speaking, Jinzhen broke down into floods of tears.
It proved impossible to console him. Whatever people said to him to try and cheer him up, it did not make the blindest bit of difference. In the end Young Lillie had simply had enough and angrily thumped his fist down on the dining table, shouting at him to control himself. Although he did stop crying at that point, it was clear that he was still terribly upset. He was holding onto his thighs, digging his nails in, as if his life depended on it. Young Lillie ordered him to keep his hands above the table. Afterwards, he spoke to him very sternly, though he was clearly intending his words to console the boy. He said, ‘What are you making that kind of racket for? I still haven’t finished speaking. When I have, then you can see if you still want to cry.’
He continued, ‘When I said that you were wrong just now, I was speaking theoretically – the fact is that you ignored the existence of leap years. On the other hand if you look at it from the point of view of mathematics, it would be impossible to say that you were wrong, because there are acceptable errors in any calculation.
‘According to my knowledge, the time it takes the earth to complete one orbit of the sun is three hundred and sixty-five days, five hours, forty-eight minutes and forty-six seconds. So why do we need leap years? There is a simple reason: according to the solar calendar, every year there are five extra hours, whereby every four years you need a leap year which consists of three hundred and sixty-six days. However, as I am sure you will realize if you think about it, if you calculate that ordinary years consist of three hundred and sixty-five days and that each leap year contains three hundred and sixty-six days, you are still not going to obtain a completely accurate calculation. It is convenient for most ordinary purposes to let the mistake go by; in fact, it would be impossible to work the solar calendar without this acceptable error. What I am trying to tell you is that even if you had allowed for leap years, your calculation would still be wrong.
‘Now you can go away and work out how many leap years Mr Auslander lived through during his eighty-nine years and then add that number of days to your original calculation. Then you can work out how big the difference is between your original calculation and the new one. In a calculation involving figures of more than four places of decimals, the acceptable margin for error is normally set at 0.01 per cent; any more than that and you have made a mistake in your calculations. Right: now you tell me, is your mistake within the acceptable margin for error?’
Mr Auslander died in a leap year at the age of eighty-nine, thus he had lived through twenty-two leap years: that does not sound many, but it is also not a few. Adding one day for every leap year means that twenty-two leap years is equivalent to twenty-two days. Adding that to the more than 30,000 days that Mr Auslander had spent on this earth meant that it was a mistake well within the acceptable margin of error. The reason why Young Lillie made such a point of this is that he wanted Jinzhen to find a way to forgive himself for the mistake that he had made. Thanks to the way that Young Lillie first shouted at him and then cajoled him, Jinzhen finally calmed down.
[Transcript of the interview with Master Rong]
Later on, Daddy explained to us how Mr Auslander had asked Zhendi to work out his age. Thinking of how upset he had been, I suddenly found myself feeling moved by his obvious affection for the old foreign gentleman. On the other hand I also realized that he had an obsessive streak in his character – not to mention an inability to cope with his own mistakes. Later on we realized more and more clearly that Zhendi could on occasion be really stubborn and fierytempered; most of the time he was so quiet and kept himself to himself. He could put up with all sorts of things and simply carry on as if nothing had happened – in fact he could tolerate things that most people would find absolutely unendurable. But once an invisible line was crossed, once something had touched the most delicate part of his psyche, he would lose control very easily. This loss of control was always expressed by some extreme act. I could give you lots of examples of this kind of thing. For example, he really loved my mother and so one day he wrote a message in his own blood, completely in secret. What he said was: ‘Daddy is dead. The rest of my life is going to be devoted to looking after Mummy.’
When he was seventeen, he got terribly sick and spent a long time in hospital. Mummy discovered this note then, because she was forever popping into his room to look for something or other that he wanted. It was slipped inside the binding of his diary and written in large characters. It looked as though he had used the tip of a finger to write it, but there was no date on it, so we didn’t know when it had been written. It was clear that it was not recent, so I reckon that he probably wrote it during the first year or two that he was living with us. The foxing on the paper and the fading of the characters certainly suggested that it had been there for some time.
My mother was a very kind and gentle woman, friendly with everyone. She remained the same throughout her long life. When you think about her relationship with Zhendi, it really seemed as though they were destined to be friends, because the two of them got along amazin
gly well right from the very beginning. They had the kind of silent rapport that you normally only see among close family members. From the very first day that he came to live with us, Mummy called him Zhendi. I don’t know why she called him that; maybe it was because my little sister had only just passed away and she was transferring all her affection to him. After my sister died, Mummy didn’t set foot outside the house for the longest time; she just sat at home and mourned. Many nights she had nightmares, and during the day she often imagined that she saw my dead sister. Once Zhendi arrived, Mummy gradually recovered. Maybe you don’t know this, but Zhendi knew how to interpret people’s dreams. He was wonderfully good at it, just like visiting a professional shaman. He was a Christian though and read a little English-language Bible every day, even though he knew lots of passages completely off by heart. I think that the reason Mummy recovered so quickly and with so few setbacks along the way was entirely thanks to the fact that Zhendi was there interpreting her dreams for her and telling her stories out of the Bible. It is hard to explain exactly why they got on so well together. Of course, Mummy loved Zhendi; she always thought of him as one of the family and respected and cared about him. What nobody knew at the time was how deeply Zhendi was affected by this and how he became determined to repay her for everything that she did for him. That is why he secretly wrote that message in his own blood. In my opinion, Zhendi had lacked affection in his earlier life; in particular he had never experienced mother-love. Everything that Mummy did for him – cooking him three meals a day, making his clothes, asking him if he was too hot or too cold – this was all new to him and he felt it deeply. As time went on and more and more things were done for him, he wasn’t able to deal with his emotions any more and found this way of expressing his gratitude. Of course, the way that he chose was more than a little melodramatic, but that is the kind of boy he was. If I may be allowed the benefit of hindsight, I think that nowadays we would say that Zhendi was autistic.
I could cite lots of other examples of similar kinds of behaviour, and perhaps I will tell you about them later on. However right now we need to go back to the evening when he had hysterics, because the matter is not yet over . . .
[To be continued]
The following evening, again at suppertime, Jinzhen returned to the matter that had been under discussion the previous day. He said that Mr Auslander had lived through twenty-two leap years and hence it might appear that he had got his figures out by twenty-two days, but that in fact he was only wrong by twenty-one days. That seemed completely stupid! If you have lived through twenty-two leap years then that adds one day for every year – it should be twenty-two days. Why did he say that it was twenty-one? Everyone, including Mrs Lillie, thought that he must have gone off his head. But when Jinzhen explained what he meant, those present realized that he had a point.
You see, Young Lillie had explained that leap years were introduced because in fact each year is 365 days, 5 hours, 48 minutes and 46 seconds long, and thus every four years they add another 24 hours. But obviously it is not precisely 24 hours that needs making up, because that would require the earth to take 365 days and 6 hours to travel once around the sun. How much is the error introduced? Every year it is 11 minutes and 14 seconds, so in other words over the course of four years, an error of 44 minutes and 56 seconds is introduced. This means that in every leap year cycle, a certain amount of time is added: 44 minutes and 56 seconds. Mankind steals that time from the earth. Mr Auslander lived through twenty-two leap years, so for him, a total of 16 hours, 28 minutes and 32 seconds of non-existent time had been added to his life.
However, as Jinzhen pointed out, according to the original figure Mr Auslander had lived for 32, 232 days, a number that he obtained not by working out how many days there were in eighty-eight years, but how many days there were in eighty-eight years plus 112 days. While it was perfectly true that when he was calculating the 112 extra days he ignored the existence of leap years, it is also a fact that a day is not precisely twenty-four hours long. In actual fact a day is twentyfour hours plus almost a minute long – over the course of 112 days that would add up to 6,421 seconds, or in other words one hour and forty-seven minutes. So you have to deduct that one hour and fortyseven minutes from the original figure of 16 hours, 28 minutes and 32 seconds, which gives you a new total of 14 hours, 41 minutes and 32 seconds. That gives you the real figure for the non-existent time added to Mr Auslander’s life by the modern calendar.
Jinzhen went on to say that according to his information, Mr Auslander had been born at noon and he died at nine o’clock in the evening, so at the beginning and end of his life, there was at least ten hours of non-existent time being factored in, not to mention the 14 hours, 41 minutes and 32 seconds that he had accumulated during his lifetime. No matter how you worked it out, Mr Auslander had one whole day’s worth of non-existent time added to his lifespan. Jinzhen had clearly spent a lot of time thinking about what a leap year meant. You could say that since the existence of leap years had put his calculation of the number of days that Mr Auslander spent upon this earth out by twenty-two days, now he had got his own back by cutting down his mistake by twenty-four hours.
According to Master Rong, she and her father were both amazed at this development. They both felt impressed and moved by this evidence of the boy’s crystal-clear intellect. However, the most amazing thing was yet to come. A couple of days later, when Master Rong had just arrived back home in the afternoon, her mother (who was cooking downstairs) told her that her father was in Zhendi’s room and that she was to go and join them. When Master Rong asked why, her mother said that Zhendi seemed to have come up with some kind of mathematical theorem and that her father had been absolutely stunned.
As mentioned before, since the last 112 days of old Mr Auslander’s life had originally not been calibrated to take account of the existence of leap years; if you insist that each day consists only of twenty-four hours, in fact you are leaving 1 hour and 47 minutes, or 6,421 seconds, unaccounted for each year. The error introduced annually is 6, 421 seconds. In the cycle of one leap year, you can deduct the uncounted time from the non-existent time: –6,421 + 2,696 seconds, where 2,696 represents the number of seconds in 44 minutes and 56 seconds. In the second leap year cycle, the amount of non-existent time is (–6,421 + 2 x 2,696) seconds, and so on and so forth until you arrive at the calculation for the last leap year: (–6,421 + 22 x 2,696) seconds. Jinzhen had calculated the missing time, unaccounted for in his original figure for how many days Mr Auslander had lived, which he worked out as 88 years and 112 days, or 32,232 days, into twenty-three lines of elegant calculations, to wit:
(–6,421)
(–6,421 + 2,696)
(–6,421 + 2 x 2,696)
(–6,421 + 3 x 2,696)
(–6,421 + 4 x 2,696)
(–6,421 + 5 x 2,696)
(–6,421 + 6 x 2,696)
. . .
(–6,421 +22 x 2,696)
Based upon this, and without any instruction from anyone, he had gone on to work out a mathematical formula:
X = [(first value + last value) x number] / 2* He had managed to work out a mathematical formula completely unaided.
[Transcript of the interview with Master Rong]
Mathematical formulae are not such bizarre and abstruse things that ordinary people cannot work them out. The fact is that anyone with a good knowledge of mathematics could reframe their knowledge in the shape of a formula – provided that they know that formulae exist in the first place. I could shut you up in a dark room, having told you in considerable detail about its contents. If I then demanded that you find me a particular object, even though the room was pitch-dark, you might well still be able to find it. If you used your intelligence, if you moved your feet carefully and felt with your hands, gradually working out what things have been put where, you ought to be able to find what I have asked you to look for. On the other hand if I had not told you what was in the room in the first place and then demanded that yo
u go and find me a particular object, the chances are that you would not be able to do it.
Well, if he had been faced with a simple list of numbers, like say 1, 3, 5, 7, 9, 11 (not something complicated and irregular) and he had worked out a mathematical formula for that, it would have been much more easy to understand and we wouldn’t have been quite so amazed. You could compare this to someone making a piece of furniture from scratch without a single lesson from a carpenter. It doesn’t matter that other people have made the same piece many times before:
* Conventionally, this formula would be given as: S = [(A1 + An) x n] / 2.
we would still be impressed at your abilities. If the tools and material at your disposal were of poor quality, if the tools were rusty and the wood rough, and yet you still managed to produce a decent piece of furniture, we would all be doubly impressed. That is what Zhendi had done: he had effectively taken a stone hand-axe and a tree standing in the forest and turned them into a beautiful piece of furniture. We were that amazed, we could hardly believe the evidence of our own eyes. It was completely unbelievable!
After this, we felt that it would not be a good idea to keep him on at primary school, so Daddy decided to enrol him in the middle school attached to N University. The school was only a couple of doors down from our house, so if he went there as a boarder, it would quite possibly be even more damaging to Zhendi’s fragile psyche than if we had just thrown him out onto the streets. So, at the same time as Daddy decided to enrol Zhendi in the first year at middle school, he also decided that he would have to continue living with us. The fact is that after Zhendi came to live with us that summer, he never left until he got his first job . . .
[To be continued]
Children like giving each other nicknames; any child in the least bit peculiar will find himself being given a nickname by his classmates. When the other pupils at the school first caught sight of Jinzhen’s huge head, they called him ‘Big-head’. Later on they realized that he had all sorts of peculiar habits – like he really enjoyed counting the hordes of ants that marched backwards and forwards across the playground and was completely oblivious to anything else while he was doing it, or that in the winter he would always wear a tatty old scarf trimmed with dog-fur (apparently this had been a present from old Mr Auslander), or that he would fart and belch in class, without the least sign of restraint, just letting it all hang out as it were. People really did not know how to take him. Another thing: he always wrote his homework in duplicate – once in Chinese and once in English. What with one thing and another, people felt that there was something wrong with him, that he must be stupid. But at the same time his grades were fantastic, really impressive, better than what the rest of the class could achieve put together. So they came up with a new nickname for him, ‘Idiot-savvy’ by which they meant ‘idiot savant’. This nickname was particularly apposite because it encompassed his behaviour both inside and outside the classroom. Like many nicknames it seemed to denigrate its possessor, but at the same time it had an element of praise – a perfect mix of contempt and respect: everyone felt it was the right name for him. Everyone called him that.