J. Coetzee - The Schooldays of Jesus

‘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 Davíd, 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 Davíd 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’ offer to the few fruit-pickers left on the farm, but when the time comes for the first lesson Davíd 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, Davíd, 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 important 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?’