Exploring the (Sort of) Infinite

Defining the Infinite (?)

Infinity is a tricky concept. In one sense it is the total — after all, there is nothing bigger than it — and so a closed concept, the end of the line. Then again it seems to be very open — there is always something more to it, it seems inexhaustible — to defy ending.

Once we get a sense of how different people are, and how different are our responses, we can have a sense that there is an infinity of possible interpretations for any particular word or statement. A friend of mine hates the smell of fresh bread. (His mother smuggled it during wartime to those opposing the occupying power. The smell of bread is associated with incredible anxiety, and so he doesn’t like it). It is tempting to think that any particular sensation can be associated with anything — that the possibilities are infinite.

And yet the impossibilities are infinite, too. This is especially true where there are particular “rules of the game” and defined contexts, such as in the grammar of a language. While it is true that interpretations of a phrase, like “the snow is white” may be various, there are also infinite interpretations that don’t apply, such as “please buy some bread on your way home”.

Curiously, infinity (of possibilities) minus infinity (of impossibilities) does not seem to equal zero. Infinity is a very tricky concept for me to wrap my head around.

However, I do have a rough and ready definition of what is effectively infinite: infinity is what I can understand plus a bit. I find this useful in relationships with people and situations I am involved in.

Infinite People

People are effectively infinite. I have never known anyone who was entirely predictable. They always have the ability to surprise me.

Part of the reason for this I think is that we (often at least) have an experience of choice. That is, we feel that we could do something different than what we are doing — to stop if we are walking, to speak more emotionally or rationally than we currently are, or to be more or less kind than we currently are.

This experience of choice usually means that there are possibilities open to us to do something other than what we are doing. We may not choose to pursue these possibilities, but they usually exist.

It seems to me that this is a basis for a profound hope. This hope has been justified in my experience by those who have healed from pasts of truly appalling suffering. In an even more extreme form (a death camp), Victor Frankl pointed out in Man’s Search for Meaning [Amazon-US | Amazon-UK] that when everything is stripped away from a person, not everyone behaves as a devil — some behave like angels. And it seems impossible to predict who will recover or who will act like an angel, or a devil.

It seems that the possibilities of a person are infinite. A philosopher named Levinas has written a very difficult book about this, called Totality and Infinity [Amazon-US | Amazon-UK] — at least it is very difficult for me to read. His case, as I understand it — and people who can read (this kind of) philosophy tell me I am on the right track — is that the person is infinite: they cannot be contained by any category. Meeting someone face to face overflows and breaks through any category we may assign them. It is an extraordinarily stimulating book, but a very long way from an easy read, at least for me.

Infinity in Situations

Not only do people surprise us, but there are usually overlooked possibilities in our situation. One way we discover this is by talking to others about a situation we are in. Often others will have a different way of evaluating or thinking about the situation we are struggling with.

The arts show us that there is a kind of infinity too. There still seem to be as many pictures to be painted as there ever were, and as many tunes to be played. This is most directly experienced in music during improvisation. There are only so many notes, and yet there seems an infinity of possibilities when we hear a great jazz player improvising. In classical music too, there are pieces like Bach’s Goldberg Variations where one tune seems capable of infinite variations. Any master of an art seems capable of continually surprising us — continually finding freshness even within a very restricted discipline (Piet Mondrian is a painter who used black horizontal and vertical lines on a white background and blocks of primary colour — and yet no two of his paintings are the same.)

This too seems profoundly hopeful to me. In any situation there are likely to be unexplored possibilities. If I am talking to someone and I feel that I have no ideas, I have found that there is a way to free up my thinking. This is to say something like, “I don’t know, I can’t think of anything”. This is usually enough to free up my thinking.

This is a daily experience for me in writing. I have a fairly narrow set of interests — health, with an emphasis on self-development. And yet I find that there is a wealth of material — I have never run out of stuff to write about. Even in this one narrow topic there is an effective infinity of topics to write about.

Creating Our Lives

In a sense, we improvise our way through life. We select from the (effectively infinite) possibilities in ourselves, our relationships, our circumstances. In one sense, while we are alive we are occupied with exploring the infinite. And it seems to me that this can be profoundly hopeful.

I would like to know how you respond to this idea of improvising our way through life, of exploring a life that is (effectively infinite). It may be that your sense is exactly the opposite to mine. If so I’d love to hear about this too. I look forward to hearing from you in the comments.