There are, I come to realise, an infinite number of infinities.
When I put this to my young Mathematician Friend as a question, he interprets it mathematically and gives me an explanation I do not comprehend, but of which I have a faint feeling it appertains to something entirely different, though nonetheless relevant and important. Maybe I did not phrase my question well, and he did not understand it. Or very possibly he did fully understand the question and gave me a perfectly valid answer, but one that makes sense to his young mathematician mind more than it does to mine, which is twice as old and really not scientific at all.
I have enjoyed my young Mathematician Friend’s company, and I miss him and think of him often. He has a lovely smile, though it be slightly downward inclined, which makes him look just a tad sceptical when he smiles. Then again, he is a mathematician, so he has every right to be sceptical, and his smile is no less lovely for it.
I am fairly convinced that since there are more infinities than just one, there may well be several, and if there are several, there may well be many, and if there are many, then conceptually it strikes me as obvious that most likely there are an infinite number of infinites. Not being a mathematician, or at all scientifically minded, I only know of three infinities, two of which are of the same kind, and a third that is of an entirely different kind.
The reason I know that there are more infinities than just one is that there is the infinity of rational numbers, which perch on the unending line in the plus/minus direction where you can always add one more or take one more away. This means you in a sense already have two infinites, a positive and a negative one, but they are, in character, the same and should therefore probably be considered, if not one, then of one ilk.
But there are also the irrational numbers, which, like anchor points or switches on that line stretching from negative infinity into positive infinity, branch off into another direction, or even dimension, by leading into the unending sequence of never repeating numerals after the decimal point, which we can’t simply add to or take away from, but have to calculate, and which is therefore specific but unpredictable, but predictably unending.
So, simply looking at these two types of infinity, which are easy enough to understand though they may not be instantly recognisable, my hunch is chances are there are perhaps—I would venture quite probably, so probable as to seem certain—other infinities that may be even less easy to recognise, but that are nonetheless real, as real as these two (which could be looked on as three); and so, since there are an infinite number of numbers and an infinite number of ways we can configure these numbers to express an infinite number of things, there are likely, I like to think, to the level of this being probable, and in fact quite possibly so probable as to seem certain, not just two, or three or four, or one or two dozen, but an infinite number of infinities, not least because there are bound to be an infinite number of universes.
The thought that there are an infinite number of infinities to me is beautiful because I like the idea of infinities, but it is also tiring, because while I can imagine the one or two infinities that I’m already familiar with, I can barely conceive of any beyond that; and right now I wish I could have my young Mathematician Friend with me and curl up with him, just to feel his calm body in the presence of his beautiful mind and know that there is someone who may not see the world quite as I do, but who can handle abstraction and make something of it.
We spend some time together at the Science Museum, and on my terrace, and in my bed, and then he goes back to Austria, where he’s from; and I think, this is true: we actually met on a park bench in Kensington Gardens. It feels like we’ve known each other for years, but we really just met last Thursday by the Italian fountain, when he asked me for a light, and we talked and exchanged numbers.
I lost sight, a little, of my young Mathematician Friend, after he left London, but he didn’t entirely escape from my mind, and so we met up again a few months later, this time in Vienna. That was a little strange, because now a few things had happened—none of them to do with me—that had troubled this beautiful mind of his, and while he was better again, in fact well, I now worried about him, and we talked about all manner of things, but not infinities. And then we spent a whole night together, first going out, drinking many pints of stout in an Irish pub, and then at a nice little hotel, and I thought no more of or about it, until it occurred to me that this, probably, is what most of life is mostly about: chance encounters, and where we take them, if anywhere at all.
We didn’t take our encounter much further, my Mathematician Friend and I, but that matters not; what matters is merely that we made ourselves some memories on a pin prick of an infinite number of possibilities, and for that alone I like him still.