She has definitely taken an interest in mathematics, my little neighbour. Following on from our discussion on rotational symmetry she approached me as I trimmed a tree last night and asked, 'Andrew... What do you think your house number divided by nothing equals?'
'Eh?' I said, thinking fast and suspecting a trick.
'Your house number...' she continued. 'Or my house number... or any number, divided by nothing, I mean by zero... What do you think it equals?'
I decided to cover more than one option.
'What I think,' I responded carefully, 'is that to divide any number by zero is meaningless, because, thinking about it in the other direction, to ask how many times nothing must be multiplied by to equal something, is meaningless... but, I do know that some people might claim that any number divided by nothing equals infinity, but then I think infinity is pretty meaningless too, really.'
'Well done!' she said, and I wondered if I should be pleased or insulted to have my mathematical opinions praised by an 11 year-old.
'Well done,' she said again, 'because our teacher was saying that to us today, but he said that some people would disagree about it being meaningless.'
'So what do you think about infinity?' I asked.
'Well...' she began cautiously, 'I think that if it exists it goes on for a long, long, long, long, time... But I actually think that it might be meaningless too.'
'Ah, I think you might be right, but I don't know.'
'No, neither do I.'
'So we agree?'
'Yes we do!'
And then she referred back to a discussion we had some years earlier, I think, when she asked, 'You don't believe in God do you?'
At least I think that she was thinking back to our previous conversation on that topic, and I could see the link.
'No I don't,' I responded, 'but then I don't know what the word God really means. But not knowing means not believing, I think.'
'No,' she said. 'I'm still thinking about it though.'
And I decided to say nothing and just leave her to think.
Conversations with my little neighbour are going to be quite interesting this summer, I think.