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 to mine.
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 downwards 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, because if you have an infinity that goes into one direction, such as is the case with rational numbers, which perch on the unending line of numbers in the plus/minus direction where you can always add one more, and you have another infinity, such as with irrational numbers, which, like anchor points or switches on that line, branch off in another direction or even dimension, by leading into the unending line of never repeating numerals after the decimal point that we can’t simply add to but have to calculate, and which is therefore specific but unpredictable, but predictably unending, then you can have other infinities and these infinities may not be instantly recognisable but chances are they are nonetheless real, as real as these two; 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, not just two, or three or four, or one or two dozen, but an infinite number of infinities.
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.
I sense that I need an early night and I go to sleep.