‘I am no expert on education, Inés. All the families I know in Estrella send their children to normal schools. But I am sure the academies teach the basics—you know, reading and writing and so forth. I can ask the sisters if you like.’
‘What about the Atom School?’ he asks. ‘What do they teach there?’
‘They teach about atoms. They watch the atoms through a microscope, doing whatever it is that atoms do. That is all I know.’
He and Inés exchange glances. ‘We will keep the academies in mind as a possibility,’ he says. ‘For the present we are perfectly happy with the life we have here on the farm. Do you think we can stay on after the end of the harvest if we offer the sisters a small rental? Otherwise we will have to go through the rigmarole of registering with the Asistencia and looking for a job and finding a place to live, and we are not ready for that, not yet—are we, Inés?’
Inés shakes her head.
‘Let me speak to the sisters,’ says Roberta. ‘Let me speak to señora Consuelo. She is the most practical. If she says you can stay on the farm, then maybe you can give señor Robles a call. He offers private lessons and doesn’t charge much. He does it out of love.’
‘Who is señor Robles?’
‘He is the water engineer for the district. He lives a few kilometres further up the valley.’
‘But why would a water engineer give private lessons?’
‘He does all kinds of things besides engineering. He is a man of many talents. He is writing a history of the settlement of the valley.’
‘A history. I didn’t know that places like Estrella had a history. If you give us a telephone number I will get in touch with señor Robles. And will you remember to speak to señora Consuelo?’
‘I will. I am sure she won’t mind if you stay here while you look for something more permanent. You must be longing to move into a home of your own.’
‘Not really. We are happy with things as they are. For us, living like gypsies is still an adventure—isn’t it, Inés?’
Inés nods.
‘And the child is happy too. He is learning about life, even if he doesn’t go to school. Will there be jobs around the farm that I can do to repay your kindness?’
‘Of course. There are always odd jobs.’ Roberta pauses thoughtfully. ‘One more thing. As I am sure you know, this is the year of the census. The census-takers are very thorough. They call at every farm, even the remotest. So if you are trying to dodge the census—and I am not saying you are—you won’t succeed by staying here.’
‘We are not trying to dodge anything,’ says he, Simón. ‘We are not fugitives. We merely want what is best for our child.’
The next day, in the late afternoon, a truck pulls up at the farm and a large, florid-faced man alights. He is greeted by Roberta, who leads him to the dormitory. ‘Señor Simón, señora Inés, this is señor Robles. I will leave the three of you to discuss your business.’
Their discussion is brief. Señor Robles, so he informs them, loves children and gets on well with them. He will be happy to introduce young David, of whom he has heard glowing praise from señora Roberta, to the elements of mathematics. If they agree, he will stop at the farm twice a week to give the boy a lesson. He will not accept payment in any form. It will be reward enough to have contact with a bright young mind. He himself, alas, has no children. His wife having passed on, he is alone in the world. If among the children of other fruit-pickers there are any who would like to join David in his lessons, they will be welcome. And the parents, señora Inés and señor Simón, may of course sit in too—that goes without saying.
‘You won’t find it boring, teaching elementary arithmetic?’ asks he, señor Simón, parent.
‘Of course not,’ says señor Robles. ‘For a true mathematician the elements of the science are its most interesting part, and instilling the elements in a young mind the most challenging undertaking—challenging and rewarding.’
He and Inés pass on señor Robles’s offer to the few fruit-pickers left on the farm, but when the time comes for the first lesson David is the only student and he, Simón, the only parent in attendance.
‘We know what one is,’ says señor Robles, opening the class, ‘but what is two? That is the question before us today.’
It is a warm, windless day. They are seated under a shady tree outside the dormitory, señor Robles and the boy on opposite sides of a table, he discreetly to one side with Bolívar at his feet.
From his breast pocket señor Robles takes two pens and places them side by side on the table. From another pocket he produces a little glass bottle, shakes out two white pills, and places them beside the pens. ‘What do these’—his hand hovers over the pens—‘and these’—his hand hovers over the pills—‘have in common, young man?’
The boy is silent.
‘Ignoring their use as writing instruments or medicine, looking at them simply as objects, is there some property that these’—he shifts the pens slightly to the right—‘and these’—he shifts the pills slightly to the left—‘have in common? Any property that makes them alike?’
‘There are two pens and two pills,’ says the boy.
‘Good!’ says señor Robles.
‘The two pills are the same but the two pens aren’t the same because one is blue and one is red.’
‘But they are still two, aren’t they? So what is the property the pills and the pens have in common?’
‘Two. Two for the pens and two for the pills. But they aren’t the same two.’
Señor Robles casts him, Simón, an irritated glance. From his pockets he produces another pen, another pill. Now there are three pens on the table, three pills. ‘What do these’—he holds a hand over the pens—‘and these’—he holds a hand over the pills—‘have in common?’
‘Three,’ says the boy. ‘But it’s not the same three because the pens are different.’
Señor Robles ignores the qualification. ‘And they don’t have to be pens or pills, do they? I could equally well replace the pens with oranges and the pills with apples, and the answer would be the same: three. Three is what the ones on the left, the oranges, have in common with the ones on the right, the apples. There are three in each set. So what have we learned?’ And, before the boy can answer, he informs him what they have learned: ‘We have learned that three does not depend on what is in the set, be it apples or oranges or pens or pills. Three is the name of the property that these sets have in common. And’—he whisks away one of the pens, one of the pills—‘three is not the same as two, because’—he opens a hand in which nestle the missing pen, the missing pill—‘I have subtracted an item, one item, from each set. So what have we learned? We have learned about two and about three, and in exactly the same way we can learn about four and five and so on up to a hundred, up to a thousand, up to a million. We have learned something about number, namely that each number is the name of a property shared by certain sets of objects in the world.’
‘Up to a million million,’ says the boy.
‘Up to a million million and beyond,’ agrees señor Robles.
‘Up to the stars,’ says the boy.
‘Up to the number of the stars,’ agrees señor Robles, ‘which may well be infinite, we don’t yet know for sure. So what have we achieved thus far in our first lesson? We have found out what a number is, and we have also found out a way of counting—one, two, three, and so forth—a way of getting from one number to the next in a definite order. So let us summarize. Tell me, David, what is two?’
‘Two is if you have two pens on the table or two pills or two apples or two oranges.’
‘Yes, good, nearly right but not exactly right. Two is what they have in common, apples or oranges or any other object.’
‘But it has got to be hard,’ says the boy. ‘It can’t be soft.’
‘It can be a hard object or a soft object. Any objects in the world will do, without restriction, so long as there is more than one of them. That is an importan
t point. Every object in the world is subject to arithmetic. In fact every object in the universe.’
‘But not water. Or vomit.’
‘Water isn’t an object. A glass of water is an object, but water in itself is not an object. Another way of saying that is to say that water is not countable. Like air or earth. Air and earth aren’t countable either. But we can count bucketfuls of earth, or canisters of air.’
‘Is that good?’ says the boy.
Señor Robles replaces the pens in his pocket, drops the pills back into the bottle, turns to him, Simón. ‘I’ll stop by again on Thursday,’ he says. ‘Then we can move on to addition and subtraction—how we combine two sets to get a sum, or remove elements of a set to get a difference. In the meantime your son can practise his counting.’
‘I can already count,’ says the boy. ‘I can count to a million. I taught myself.’
Señor Robles rises. ‘Anyone can count to a million,’ he says. ‘What is important is to get a grasp of what numbers really are. So as to have a firm foundation.’
‘Are you sure you won’t stay?’ says he, Simón. ‘Inés is making tea.’
‘Alas, I don’t have the time,’ says señor Robles, and drives off in a flurry of dust.
Inés emerges with the tea tray. ‘Has he gone?’ she says. ‘I thought he would stay for tea. That was a very short lesson. How did it go?’
‘He is coming back next Thursday,’ says the boy. ‘We are going to do four then. We did two and three today.’
‘Won’t it take forever if you do just one number at a time?’ says Inés. ‘Isn’t there a quicker way?’
‘Señor Robles wants to make sure the foundations are firm,’ says he, Simón. ‘Once the foundations are firmly laid, we will be ready to erect our mathematical edifice on them.’
‘What is an edifice?’ says the boy.
‘An edifice is a building. This particular edifice will be a tower, I would guess, stretching far into the sky. Towers take time to build. We must be patient.’
‘He only needs to be able to do sums,’ says Inés, ‘so that he won’t be at a disadvantage in life. Why does he need to be a mathematician?’
There is silence.
‘What do you think, David?’ says he, Simón. ‘Would you like to go on with these lessons? Are you learning anything?’
‘I already know about four,’ says the boy. ‘I know all the numbers. I told you, but you wouldn’t listen.’
‘I think we should cancel,’ says Inés. ‘It is just a waste of time. We can find someone else to teach him, someone who is prepared to teach sums.’
He breaks the news to Roberta (‘What a pity!’ she says. ‘But you are the parents, you know best.’) and telephones señor Robles. ‘We are immensely grateful to you, señor Robles, for your generosity and your patience, but Inés and I feel the boy needs something simpler, something more practical.’
‘Mathematics is not simple,’ says señor Robles.
‘Mathematics is not simple, I agree, but our plan was never to turn David into a mathematician. We just don’t want him to suffer as a consequence of not going to school. We want him to feel confident handling numbers.’
‘Señor Simón, I have met your son only once, I am not a psychologist, my background is in engineering, but there is something I must tell you. I suspect young David may be suffering from what they call a cognitive deficit. This means that he is deficient in a certain basic mental capacity, in this case the capacity to classify objects on the basis of similarity. This capacity comes so naturally to us as human beings, ordinary human beings, that we are barely aware we have it. It is the ability to see objects as members of classes that makes language possible. We do not need to see each tree as an individual entity, as animals do, we can see it as an example of the class tree. It also makes mathematics possible.
‘Why do I raise the topic of classification? I do so because in certain rare cases the faculty is weak or missing. Such people will always have difficulty with mathematics and with abstract language in general. I suspect your son is such a person.’
‘Why are you telling me this, señor Robles?’
‘Because I believe that you owe it to the boy to have his condition investigated further, and then perhaps to adjust the form that his further education may take. I would urge you to make an appointment with a psychologist, preferably one who specializes in cognitive disorders. The Department of Education will be able to provide you with names.’
‘Adjust the form of his education: what do you mean by that?’
‘In the simplest terms, I mean that if he is always going to struggle with numbers and abstract concepts, then it may be best if he goes, for example, to a trade school, where he can learn a useful, practical trade like plumbing or carpentry. That is all. I take note that you have decided to cancel our mathematics lessons, and I agree with your decision. I think it is a wise one. I wish you and your wife and son a happy future. Goodnight.’
‘I spoke to señor Robles,’ he tells Inés. ‘I cancelled the lessons. He thinks David should go to a trade school and learn to be a plumber.’
‘I wish that señor Robles was here, so that I could give him a slap in the face,’ says Inés. ‘I never liked the look of him.’
The next day he drives up the valley to señor Robles’s house and at the back door leaves a litre of the farm’s olive oil, with a card. ‘Thank you from David and his parents,’ says the card.
Then he has a serious talk to the boy. ‘If we find you another teacher, someone who will teach you just simple sums, not mathematics, will you listen? Will you do as you are told?’
‘I did listen to señor Robles.’
‘You know perfectly well that you did not listen to señor Robles. You undermined him. You made fun of him. You said silly things on purpose. Señor Robles is a clever man. He has a degree in engineering from a university. You could have learned from him, but instead you decided to be silly.’
‘I am not silly, señor Robles is silly. I can do sums already. Seven and nine is sixteen. Seven and sixteen is twenty-three.’
‘Why didn’t you show him you can do sums while he was here?’
‘Because, his way, you first have to make yourself small. You have to make yourself as small as a pea, and then as small as a pea inside a pea, and then a pea inside a pea inside a pea. Then you can do his numbers, when you are small small small small small.’
‘And why do you have to be so small to do numbers his way?’
‘Because his numbers are not real numbers.’
‘Well, I wish you had explained that to him instead of being silly and irritating him and driving him away.’
CHAPTER 4
DAYS PASS, the winter winds begin to blow. Bengi and his kinfolk take their leave. Roberta has offered to drive them to the bus station, where they will catch the bus to the north and seek work on one of the ranches on the great flatlands. Maite and her two sisters, wearing their identical outfits, come to say goodbye. Maite has a gift for David: a little box she has made of stiff cardboard, painted quite delicately with a design of flowers and tumbling vines. ‘It’s for you,’ she says. Brusquely and without a word of thanks David accepts the box. Maite offers her cheek to be kissed. He pretends not to see. Covered in shame, Maite turns and runs off. Even Inés, who does not like the girl, is pained by her distress.
‘Why do you treat Maite so cruelly?’ he, Simón demands. ‘What if you never see her again? Why let her carry such a bad memory of you for the rest of her life?’
‘I am not allowed to ask you, so you are not allowed to ask me,’ says the boy.
‘Ask you what?’
‘Ask me why.’
He, Simón, shakes his head in bafflement.
That evening Inés finds the painted box tossed in the trash.
They wait to hear more about the academies, the Academy of Singing and the Academy of Dance, but Roberta appears to have forgotten. As for the boy, he seems to be perfectly happy by himsel
f, dashing about the farm on business of his own or sitting on his bunk absorbed in his book. But Bolívar, who at first would accompany him on all his activities, now prefers to stay at home, sleeping.
The boy complains about Bolívar. ‘Bolívar doesn’t love me anymore,’ he says.
‘He loves you as much as ever,’ says Inés. ‘He is just not as young as he used to be. He doesn’t find it fun to run around all day as you do. He gets tired.’
‘A year for a dog is the same as seven years for us,’ says he, Simón. ‘Bolívar is middle-aged.’
‘When is he going to die?’
‘Not anytime soon. He still has many years before him.’
‘But is he going to die?’
‘Yes, he is going to die. Dogs die. They are mortal, like us. If you want to have a pet who lives longer than you, you will have to get yourself an elephant or a whale.’
Later that day, as he is sawing firewood—one of the chores he has undertaken—the boy comes to him with a fresh idea. ‘Simón, you know the big machine in the shed? Can we put olives in it and make olive oil?’
‘I don’t think that will work, my boy. You and I are not strong enough to turn the wheels. In the old days they used an ox. They harnessed an ox to the shaft and he walked in a circle and turned the wheels.’
‘And then did they give him olive oil to drink?’
‘If he wanted olive oil they gave him olive oil. But usually oxen don’t drink olive oil. They don’t like it.’
‘And did he give them milk?’
‘No, it’s the cow who gives us milk, not the ox. The ox hasn’t anything to give except his labour. He turns the olive press or pulls the plough. In return for that we give him our protection. We protect him from his enemies, the lions and tigers who want to kill him.’
‘And who protects the lions and the tigers?’
‘No one. Lions and tigers refuse to work for us, so we don’t protect them. They have to protect themselves.’
‘Are there lions and tigers here?’