Driving with children

On I Spy, Buzz and Prime Numbers
One of John’s nieces with her husband and three kids – eldest starting high school in 2008 – stayed with us for four days from Boxing day. A good time was had by all, going fishing, making things out of clay, eating, more eating, and finding – perhaps making – room for even more food. We did a bit of driving – a trip to Nimbin; another to the Cold Roast (Gold Coast for those no up on your Strine) with the kids swapping cars as we went. The favourite game was I Spy With My Little Eye.

It occurred me after a while that it’s a game that adults would benefit from – and about which someone could almost certainly write a thesis. I won’t go into too much detail here, but how often have you heard jaded grown ups complain about the boring car trip they had just done? That would be because they didn’t pay attention, wanting to be somewhere else, perhaps – the destination rather than the journey. Imagine the most featureless scene you have ever… well, seen… There’s always more there than immediately “meets the eye”. Actually, if something’s there, it meets the eye, given 20/20 vision, but it may not get your attention. So I Spy played in what would normally be thought of as a boring and unstimulating place will generate attention to details not normally noticed. It may even give rise to the need to name phenomena previously unknown to one or more of the players. The special challenge when driving is that one has to choose categories of objects that can be seen, while moving, for at least as long as it takes players to answer correctly or give in. The kids did this without even being aware of it – until, that is, one of them nominated something that was not observable once we had gone past it, and one of the others articulated the rule that had been implicit until that point. If I were to say to you that everything we do/know is theory-laden your eyes would probably glaze over. But I just gave you an example of what I would be talking about, were I talking about it – which I am. The kids recognised that the rules that applied in static situations would not work in dynamic situations and adopted a new set of behaviours to deal with the changed situation; and only when it became necessary, clarified the way the rules had changed. Now imagine trying to explain that to them. It can be done, but not while they’re playing the game.

Now imagine a society in which I Spy With My Little Eye is not just a game but the sacred ritual that mediates their sense of who they are, and must be played five times a day at precise times. This society existed long before there were trains cars and aeroplanes, and developed their ritual in a world that was virtually static; and concealed the fact that they developed the ritual by telling themselves – and coming to believe – that the ritual was written on a stone tablet that was lowered from heaven on a golden rope. In time their neighbours begin to travel in trains, cars and aeroplanes. But because an object cannot be seen once they have passed it, they find they cannot perform their ritual. Well, they can if they travel in cars, because they can stop while they do their thing. But trains and planes won’t stop for them, and anyway, what’s there to see at 30,000 metres, and when the train, plane and even the car takes them beyond the landscape they know to landscapes they have never seen before, and therefore cannot name, how could they play their game? What would they do? Refuse to travel in trains and planes to far away places, and travel by car only within the landscape they know? Or change the ritual? Maybe even abandon ritual altogether for want of the theory that ritual is context dependent – indeed condemning as “Modernism” such a theory when it arose. See what I mean about the potential for a thesis. And all because I overheard kids playing a game.
At the risk of frightening you to death, I want to tell you about another game that I don’t think they understood at all. It is called Buzz. One person says a number – it can be either odd or even. The other person says Buzz. The first person says another number, but if the first number was odd, the second has to be odd. If it is not, the other person has a turn. On this set of rules, the result is that someone who knows the difference between odd and even numbers and can count to 100 gets to say every odd or even number between 0 and 100 and stays in for the whole time. Boring. No one played by that set of rules for long. Which set me thinking. They must have misunderstood the rules. It would be so simple to modify them. Succeeding numbers had to be the opposite of the numbers that preceded them, for example. I say an odd number, my partner says buzz, and I must then say an even number, otherwise it is my partner’s turn. But even that can’t have been the intent of the game. What could it be? I had an idea. Maybe it was a game about Prime Numbers. So I asked the Tatum, who had just finished grade one, how many twos in four. Two, she said. How many twos in two? One. OK, I thought, she knows about division. So I said, tell me a number that can be divided with nothing left over by itself or one. What? the problem was the word divided. She knew how to do it but not how to name it. And what about “with nothing left over”? Well, I said, how many threes in eight? More than two but not three. Yes, two with something left over. Oh, yeah. OK, now tell me an number that can be divided by itself or one with nothing left over. Long pause. They all can, she said. Another long pause as I pondered what had gone wrong. I was trying to steer her towards the concept of prime numbers and was facing the prospect of all numbers being prime numbers if I didn’t refine the rules of the game. Yes, I said. Now tell me a number that can be divided only by itself or one with nothing left over. Four, she said. No. there’s nothing left over when you divide four by one and by four. But how many twos in four? Two, she said. And nothing left over, I prompted. Oh yeah. What about five? Yes. Give me another one. Not six, she said. Why? Because there are three twos in six. Correct. Another. Seven. Yes, another. Not eight. Correct. Nine she said triumphantly. There’s four twos in nine with one left over. Ah, I said, but how many threes in nine? Three, she shot back. Oh! And nothing left over. Yes. Now do you see how it works? I want numbers that can only be divided by one or themselves with nothing left over. So now we have a new set of rules for the game Buzz. I say a number and you buzz me. My next number must be one that can only be divided by itself or one with nothing left over. Long pause. Say that again. OK but before I do, lets give the numbers we’re talking about a name. What will we call them? Long pause. I don’t know, don’t they already have a name? Well, yes, actually, they do. What is it then? They’re Prime Numbers. Can we play I Spy With My Little Eye Again? We never did get to play Buzz with prime numbers. Oh, and by the way, later on I thought that maybe there are various stages to the game. First you just get odd or even numbers sorted; then deal with both; and then with primes.