the Manse, holding on to your tail end of string, and end up back at the tree. The circle you’ve walked in is the circumference. See? All the time, Edgar will be holding the ball of the string tight, so if you kept your end tight too, you would walk in a perfect circle.’
Sophia asked, ‘What’s the diameter, then?’
‘I already told you. It’s twice the length of a radius … Never mind … Look, if you really want to know, the diameter stretches from the tree, to Edgar at the gate, through the centre of the Manse and across the cemetery, into the field. You don’t need to think about the diameter, or the radius or circumference for that matter. All you need to do is walk in the circle that the tight length of string lets you make.’
‘Just walk round holding the string?’
‘Just walk round holding the string.’
‘What if I come up against weeds or a shrub too big to climb through, or stinging nettles or sinking sand? There’s an awful lot of holes and things there. I wouldn’t like to fall in. I might get trapped. Mother says to be careful.’
‘It’s all right to walk around things, but you can’t let go of the string. You must keep it as tight as you can. Well, fairly tight anyway.’
Sophia looked to me for confirmation that Gregory was making sense. I knew her thoughts: what if her walk round the Manse turned out to be zigzags or a square rather than a circle? Or a rectangle or a triangle, although Sophia might have no knowledge of rectangles and triangles – I’d go over it with her later.
Meanwhile, as I imagined Sophia circling the Manse with her string, something occurred to me which Gregory had overlooked.
‘But if Edgar’s standing at the garden gate holding the ball of string,’ I piped, commanding Gregory’s attention, ‘and if Sophia walks round the house the string will wrap round it and she’ll end up against a wall unless it’s a very big ball of string that never runs out. If there’s not enough string she’ll run out of radius.’
I looked at Sophia to see if she understood what I meant. If she did understand, I hoped she might explain it to me. With my attention elsewhere, Gregory took his opportunity and punched me in the head, which hurt him more than it hurt me because he had never broken the habit of punching with his thumb inside his fist instead of out. When he returned to the living room, after running his hand under the cold water tap, he said that we were stupid and he refused to have anything further to do with us.
Sophia and I, with Edgar’s help, attempted to create the circumference outside which Sophia had been forbidden to venture. It didn’t work. Edgar was supposed to hold his end of the string and stand still, but he kept following us.
We agreed that ‘the Manse’ meant the building and the land around it. But how much land? Could she venture into the fields behind the cemetery, or on to Hollow Heath beyond the front garden?
We understood the boundary to be a fixed boundary for all time. Children have a weak perception of change and shifting boundaries, and Sophia and I had almost none. I wanted to award her a greater range in which to roam than she felt entitled to. She would have restricted herself to the garden at the front, the cemetery at the back, and the outbuildings where Father stored his farming tools and jars of nails and rat poison. The fence round the front garden made an obvious boundary, but I saw no harm in her venturing on to the heath so long as she remained in view from the Manse.
Crossing the heath to the railway track clearly had to be forbidden; she would be too far away at the track, and out of sight to anyone looking for her without binoculars. Hollow Wood had to be out of bounds too. It was almost as far away as the railway track. We never went there anyhow. It looked dark and creepy. When the sun fell behind it, it looked like a black wall. Tramps and escaped criminals lived there. They hunted hares for food and
Sophia asked, ‘What’s the diameter, then?’
‘I already told you. It’s twice the length of a radius … Never mind … Look, if you really want to know, the diameter stretches from the tree, to Edgar at the gate, through the centre of the Manse and across the cemetery, into the field. You don’t need to think about the diameter, or the radius or circumference for that matter. All you need to do is walk in the circle that the tight length of string lets you make.’
‘Just walk round holding the string?’
‘Just walk round holding the string.’
‘What if I come up against weeds or a shrub too big to climb through, or stinging nettles or sinking sand? There’s an awful lot of holes and things there. I wouldn’t like to fall in. I might get trapped. Mother says to be careful.’
‘It’s all right to walk around things, but you can’t let go of the string. You must keep it as tight as you can. Well, fairly tight anyway.’
Sophia looked to me for confirmation that Gregory was making sense. I knew her thoughts: what if her walk round the Manse turned out to be zigzags or a square rather than a circle? Or a rectangle or a triangle, although Sophia might have no knowledge of rectangles and triangles – I’d go over it with her later.
Meanwhile, as I imagined Sophia circling the Manse with her string, something occurred to me which Gregory had overlooked.
‘But if Edgar’s standing at the garden gate holding the ball of string,’ I piped, commanding Gregory’s attention, ‘and if Sophia walks round the house the string will wrap round it and she’ll end up against a wall unless it’s a very big ball of string that never runs out. If there’s not enough string she’ll run out of radius.’
I looked at Sophia to see if she understood what I meant. If she did understand, I hoped she might explain it to me. With my attention elsewhere, Gregory took his opportunity and punched me in the head, which hurt him more than it hurt me because he had never broken the habit of punching with his thumb inside his fist instead of out. When he returned to the living room, after running his hand under the cold water tap, he said that we were stupid and he refused to have anything further to do with us.
Sophia and I, with Edgar’s help, attempted to create the circumference outside which Sophia had been forbidden to venture. It didn’t work. Edgar was supposed to hold his end of the string and stand still, but he kept following us.
We agreed that ‘the Manse’ meant the building and the land around it. But how much land? Could she venture into the fields behind the cemetery, or on to Hollow Heath beyond the front garden?
We understood the boundary to be a fixed boundary for all time. Children have a weak perception of change and shifting boundaries, and Sophia and I had almost none. I wanted to award her a greater range in which to roam than she felt entitled to. She would have restricted herself to the garden at the front, the cemetery at the back, and the outbuildings where Father stored his farming tools and jars of nails and rat poison. The fence round the front garden made an obvious boundary, but I saw no harm in her venturing on to the heath so long as she remained in view from the Manse.
Crossing the heath to the railway track clearly had to be forbidden; she would be too far away at the track, and out of sight to anyone looking for her without binoculars. Hollow Wood had to be out of bounds too. It was almost as far away as the railway track. We never went there anyhow. It looked dark and creepy. When the sun fell behind it, it looked like a black wall. Tramps and escaped criminals lived there. They hunted hares for food and
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