Monday, November 7, 2005


I was thinking about 217.

Is 217 real? I don't think it is. If you're not Rainman, you can't see 217. The numbers are entirely abstract. They don't even mean anything. Just one and one more until you get to 217. I'm guessing that's what they are. I don't know mathematics at that level. I keep meaning to read a book on mathematical principles but I can't stop the word "turgid" from bubbling up when I approach the bookshop.

Zenella is counting to a hundred. Can you count to a million? she asks. Yes, I say, because when you can count to a hundred, you can count to a million. She doesn't understand the principle of numbers, tens and units I mean, because she has not yet been taught it. I tried to explain but I don't want to make what is joyful "turgid" for her. She thinks that after 59 it's 60, 90, 100.

Let's count together to a million then, she says. It will take us a long time, I say. Maybe till next week, I say. I can't remember how long it takes to count to a million. That's a long time, she says. She doesn't quite believe me. You could count forever, I say, and you wouldn't run out of numbers. Actually, I'm not sure about that. It's my belief that infinity is more than forever, but they could be equal. It's simply that I know that time began at the Big Bang, and so it has a limit of sorts, and also that I know that the Planck limit is a definite end to how small time can be, and numbers can of course be smaller. Infinitely smaller.

But what is 217? If I had 217 dollars, I could spend a dollar and then I'd have 216, but I'm no clearer what that is. It's purely abstract, just a number in my bank account. It represents more or fewer CDs, dinners, bills paid, but in itself it's not anything.

I know what three is. There are three glasses on my desk (empty glasses -- the sun hasn't even gone past the yardarm on the way up yet!). I can see three. I think I could probably see four or five. After that I'd have to count and that isn't the same thing.

I don't know what 217 is unless it really is the functions that 217 dollars has. I know that 216 is divisible by three. Is that part of what it is? Does it exist conceptually as a multiple of three? How? A quick bit of mental arithmetic tells me that 217 is a multiple of 7. But what is that? What good does it do to know that? Would I ever gather sevens? And if I did, wouldn't it be more interesting to know how many sevens I had than how many of the things gathered I had altogether? Isn't that the point of multiples?

I am thinking I cannot think what 217 is except to think of what function it has, what it can represent. But how is that different from thinking about Mrs Zen, or Zenella, or myself? Do those things only differ from 217 in having an apparent physical presence? Would 217 things be 217? As I said, I wouldn't know that they were without taking them and counting them all. But isn't a process of inquiry part of knowing what anything is? And isn't that process of inquiry partly a question of enumeration, working out the parts? Is anything a whole thing? We learn what things are by distinguishing them from others. Isn't 217 just what it is because it is not 216?