The Schooldays of Jesus Read Online Free PDF

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.’
    â€˜Up to a million million,’ says the boy.
    â€˜Up to a million million and beyond,’ agrees señor Robles.
    â€˜Up to the stars,’ says the boy.
    â€˜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?’
    â€˜Two is if you have two pens on the table or two pills or two apples or two oranges.’
    â€˜Yes, good, nearly right but not exactly right. Two is what they have in common, apples or oranges or any other object.’
    â€˜But it has got to be hard,’ says the boy. ‘It can’t be soft.’
    â€˜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.’
    â€˜But not water. Or vomit.’
    â€˜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.’
    â€˜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.’
    â€˜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.’
    â€˜Are you sure you won’t stay?’ says he, Simón. ‘Inés is making tea.’
    â€˜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?’
    â€˜He is coming back next Thursday,’ says the boy. ‘We are going to do four then. We did two and three today.’
    â€˜Won’t it take forever if you do just one number at a time?’ says Inés. ‘Isn’t there a quicker way?’
    â€˜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.’
    â€˜What is an edifice?’ says the boy.
    â€˜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.’
    â€˜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